Calculator Tag: Measurement

Square Feet to Cubic Feet Calculator

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Square Feet to Cubic Feet Calculator

Use the calculator below to convert square feet to cubic feet by entering the area and height. You can also convert cubic feet to square feet by entering the volume and height.

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Square Feet to Cubic Feet

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How to Convert Square Feet to Cubic Feet

Before we start performing any calculations, it’s essential to understand the difference between square feet and cubic feet. Square footage is a measure of area, while cubic footage is a measure of volume.

The units of area are square lengths, such as ft2 or in2, and the units of volume are cubic lengths, such as ft3 or in3.

The image below shows the difference between the two measurements.

Because these are completely different types of measurements, you’ll need some additional data to calculate one from the other. In order to convert either way, you’ll need the height of the space or object.

To convert square feet to cubic feet using the area and height, you’ll need to use the conversion formula below.

Square Ft to Cubic Ft Formula

You can use the following formula to calculate cubic feet from square feet and height:

cu ft = sq ft × height

The volume in cubic feet is equal to the area in square feet times the height in feet. If you first need to calculate square feet, try our square footage calculator to find the area.

For example, let’s calculate the cubic footage of a 5 square foot area that is 2 feet high.

volume = 5 sq ft × 2 ft
volume = 10 cu ft

You can also use our calculator to convert square feet to cubic yards.

How to Convert Cubic Feet to Square Feet

When you know the volume in cubic feet and the height, you can rearrange the formula above to calculate square feet.

Cubic Ft to Square Ft Formula

This formula shows how to calculate an area from a volume.

sq ft = cu ft ÷ height

The area in square feet is equal to the volume in cubic feet divided by the height in feet. Check out our cubic feet calculator to find the volume of a space.

For example, let’s calculate the square footage of an area in a 15 cubic foot volume that is 3 feet high.

area = 15 cu ft ÷ 3 ft
area = 5 sq ft

You might also be interested in our linear feet to square feet calculator.

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Tank Volume Calculator

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Tank Volume Calculator

Select the style of tank and its dimensions to calculate the capacity in gallons and liters. Optionally, enter the filled depth to calculate the volume of liquid in a tank.

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Calculate Horizontal Oval Tank Volume

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How to Calculate Tank Volume

You can find the volume, or capacity, of a tank in a few easy steps. Of course, the calculator above is the easiest way to calculate tank volume, but follow along to learn how to calculate it yourself.

Step One: Measure the Dimensions of the Tank

The first step is to measure the key dimensions of the tank. For spherical tanks, find the diameter or radius. For cylindrical tanks, find the diameter or radius and length or height. For rectangular or cubic tanks, find the length, width, and height.

Step Two: Use the Applicable Tank Volume Formula

In order to calculate a tank’s capacity, you’ll need a formula for its volume. The volume formula varies for each shape of tank. See the formulas below and select the appropriate one for your tank.

Cylinder Tank Formula
tank volume = π × r2 × l

r = radius (diameter ÷ 2)
l = length (or height for a vertical tank)

Oval Tank Formula

This tank shape can be thought of as a cylindrical tank cut in half lengthwise with a rectangular tank inserted between the two halves. Therefore, the total volume is equivalent to the volume of the cylindrical part plus the volume of the rectangular part.

area = ((h – w) × w) + (π × r2)

tank volume = area × l

r = radius (width ÷ 2)
w = width
l = length
h = height

Capsule Tank Formula

This tank shape can be thought of as a sphere cut in half with a cylindrical tank inserted between the two halves. Therefore, the volume is equivalent to the volume of the cylindrical part plus the volume of the spherical part.

cylinder volume = π × r2 × l
sphere volume = 4/3 π × r3

tank volume = cylinder volume + sphere volume
r = radius (diameter ÷ 2)
l = length (or height for a vertical tank)

Rectangular Tank Formula
tank volume = l × w × h

l = length
w = width
h = height

Not finding a formula for the shape of your tank? Find even more volume formulas.

Step Three: Solve the Formula for Volume

When you have the tank dimensions and the appropriate formula to solve for volume, simply enter the dimensions into the formula and solve.

For example, let’s find the volume of a cylindrical tank that is 36″ in diameter and 72″ long.

radius = 36″ ÷ 2
radius = 18″

tank volume = π × 182 × 72
tank volume = 73,287 cu in

Thus, the capacity of this tank is 73,287 cubic inches.

Step Four: Convert Volume Units

The resulting tank volume will have the three-dimensional equivalent of the dimension’s units. For instance, if the initial tank measurements were in inches, then the volume measurement would be in cubic inches.

Depending on what you need to know the volume for, you’ll often need to convert it to different units, such as gallons or liters.

Thus, the final step is to convert the volume from one unit volumetric measurement to the desired unit. Try our volume converter to convert a volume to gallons, liters, or any other unit.

Curious how much a tank full of water weighs? Calculate it using our water weight calculator.

Frequently Asked Questions

How to read tank levels depends on the type of tank. For example, a rectangular tank of water often has notches on its side, and you can read the volume depending on which notch the water line is at.

For a pressurized propane tank, as another example, the tank often comes with a gauge that reads the percentage of remaining fuel. To calculate the tank level, just multiply that reading (as a decimal) by the total volume of the tank.

For example, if a 40-gallon tank has a reading of 60%, there are 24 gallons of propane remaining:

40 gallons × 0.6 = 24 gallons

One gallon equals 3.78541 liters. Therefore, when given a volume in liters, divide by 3.78541 to convert to gallons. For example, 20 liters equals 5.283 gallons:

20 liters ÷ 3.78541 liters per gallon = 5.283 gallons

There are several common sizes of propane tanks with various capacities:

  • A 20 lb propane tank holds 4.6 gallons of propane.
  • A 30 lb propane tank holds 7 gallons of propane.
  • A 40 lb propane tank holds 9.4 gallons of propane.
  • A 100 lb propane tank holds 23.6 gallons of propane.

Square Yards Calculator

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Square Yards Calculator

Get the square yardage of an area by entering the measurements of a space below. Optionally, enter a price per sq yd to get an estimated material cost.

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Using the Square Yardage Calculator

This calculator makes short work of figuring out the square yardage of any area for all your construction, landscaping, and craft projects, such as carpet, flooring, tiling, drywalling, gardening, and even sewing.

To quickly find the square yardage of a rectangular area, simply enter the length and width of your rectangle into the calculator above. Use any units, imperial or metric. To estimate costs, enter the price per sq yd. The calculator will instantly give you the necessary square yardage of the material, as well as its cost.

How to Find Square Yards

Square yardage is a common measurement of area and is used in many fields. One square yard is equal to 9 square feet, or an area that is three feet wide by three feet long.

To calculate square yardage, you must first convert your measurements to yards. You can use our length converter for a quick conversion, or, if you already know the area in sq ft, use our square feet to square yards calculator for instant results.

Diagram demonstrating that 1 square yard is equal to a 3 ft x 3 ft square, or 9 sq ft

Use these steps to calculate the area of a rectangular space in square yards.

  • Measure the length and width of each side of the rectangle
  • Convert these measurements to yards as described above.
  • Multiply the length times the width to get the area measurement in sq yds.
sq yds = lengthyds × widthyds

How to Find Square Yards Using Measurements in Feet

The steps above guide you to convert all measurements to yards before multiplying, but it’s possible to find square yards after multiplying if all of your measurements are in feet too. Follow these steps if all of your measurements are in feet:

  • Multiply the length in feet times the width in feet to find the area in square feet
  • Divide the area by 9 to find square yards.
sq yds = (length ft × width ft) ÷ 9

Formulas to Find Square Yards

The following formulas show how to calculate area in square yards for various shapes. Formulas to find the area in square yards are provided for measurements given in yards or feet to simplify conversion.

Rectangle

sq yds = lyds × wyds
sq yds = lft × wft ÷ 9
l = length
w = width

You can also use our rectangle area calculator.

Rectangular Border

sq yds = (lyds × wyds) – (ayds × byds)
sq yds = ((lft × wft) – (aft × bft)) ÷ 9
l = outer length
w = outer width
a = inner length
b = inner width

Circle

sq yds = πryds2
sq yds = πrft2 ÷ 9
r = radius
π = 3.14159265359

If you know the diameter of the circle, you can find the radius by dividing the diameter in half. You can also use our circle calculator to find the radius.

Triangle

s = 1/2(ayds + byds + cyds)

sq yds =√s(s – a)(s – b)(s – c)

s = 1/2(aft + bft + cft)

sq yds =√s(s – a)(s – b)(s – c)÷ 9

a = edge a
b = edge b
c = edge c

Our area calculator has formulas for many more shapes.

Frequently Asked Questions

An area that is 12 feet by 12 feet is equivalent to 144 square feet or 16 square yards.

While square meters and square yards are both units of area, the former is part of the metric system of units, while the latter is part of the imperial system. They are similar units, but do differ by almost 20%. For example, one square meter equals roughly 1.196 square yards.

Any area can be measured in square yards, but typically square yardage is used in housing, landscaping, and agricultural projects. It’s also commonly used to measure flooring and textiles.

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Square Meters Calculator

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Square Meters Calculator

Enter the length and width to find the area in square meters. Optionally estimate cost by adding the price per sq m.

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How to Calculate Square Meters

You might find yourself needing the area of a room or other space in square meters for a flooring, renovation, or landscaping project. To obtain such a measurement, you can measure the area of the space in square meters in a few simple steps. Follow along to learn how to calculate it yourself, or simply use the calculator above.

Step One: Measure Length and Width

In order to calculate the area of a space, you must know its dimensions. For example, if the shape of the space is a square or rectangle, then start by measuring the length and width of the space in meters using a tape measure or other measuring tool.

If your measurements are in another unit of measure, centimeters, for example, then you can either convert them to meters first, or you can find the area in another unit and convert to square meters. We have some simple area conversion utilities, or you can convert yourself. If your length measurements are in centimeters, then divide by 100 to get meters.

If your area measurement is in square centimeters, then divide by 10,000 to get square meters.

If your space is not a square or rectangle, you may need to use a formula to calculate the area of a different shape. Or continue reading to see how to measure the area of oddly shaped rooms.

Step Two: Multiply Measurements Together

Once you have your measurements in meters, you can use the appropriate formula to calculate the area of the space in square meters. Continuing the example above for the square or rectangular room, now that you have a length and width measurement, you can find the area in square meters by multiplying the length and width together.

square meters = length × width

Measuring Oddly Shaped Rooms

Often you’ll need to measure a space that’s not a perfect rectangle. It might be easiest to try to split up oddly shaped areas into separate shapes and measure the square meters of each of them separately.

Once that is complete, add up the individually calculated areas to find the total area of the space. You’ll also find that the formula above works great for rectangular areas. For other shapes, try our area calculator.

For example, see the formula below to see how to add two individually calculated areas of a complex space together.

total square meters = area 1 + area 2

If you’re interested in calculating square footage, give our square feet area calculator a shot.

Frequently Asked Questions

No, square meters are a two-dimensional unit of area, whereas meters are a one-dimensional unit of length.

One square meter is equal to a square that is 1 meter in width by 1 meter in height. For visual reference, a guitar is about 1 meter in length, so 1 square meter is approximately the area inside of a square made with guitars for edges.

You can use square meters anytime you wish to know the area of a space. Square meters are typically used for flooring, landscaping, and agricultural purposes.

A 10 m x 10 m room has an area of exactly 100 square meters, as shown by:
10 m × 10 m = 100 sq m

“Per square meter” is used whenever you are dividing some quantity by a total area, measured in square meters, for instance to find a unit price. For example, if you want to resurface a 10 square meter room and the total cost is $5,000, then the price per square meter is $500:

$5,000/10 sq m = $500 per square meter

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Square Inches Calculator

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Square Inches Calculator

To calculate the area in square inches, enter the length and width in the calculator below.

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square footage calculator

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How to Calculate Square Inches

Square inches are a unit of area measurement of a space. They are also referred to as inches squared. One square inch is equal to the area of a square with each side equal to one inch in length.

Of course, not all areas are perfect squares, but you can still calculate the area in square inches of a variety of shapes. For example, calculating the area of a rectangular shape can be done in a few easy steps.

Step One: Measure the Length and Width

The first step to calculate the area of a rectangle in square inches is to measure the length and width of the area in inches using a ruler or tape measure.

If your measurement is in another unit of measure, such as centimeters, then you’ll need to convert to inches first. Use our length converter to convert your units to inches.

Step Two: Multiply the Length and Width

The next step is to multiply the length and width to obtain the result in square inches. The square inches formula is:

square inches = length × width

Thus, the area is equal to length times width, both measured in inches. This is the same formula used to calculate square footage, except there the units of length and width are in inches rather than feet.

Square Inches Formulas

If the area for which you are trying to calculate is not a rectangle, you can instead use the appropriate formula below to find the area in square inches for several shapes. Remember, in order for the area to have units of square inches, the dimensions of the shapes must be measured in inches.

Rectangle or Square
sq in = l × w

l = length
w = width

Circle
sq in = πr2

r = radius
π = 3.14159265359
Try our circle area calculator.

Triangle
sq ft = bh/2

b = base
h = height

If you don’t know the height of the triangle, you can find it using the length of its sides.

a = edge a
b = edge b
c = edge c

Try our triangle area calculator.

You can use our area calculator to find the formulas for more shapes.

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Square Footage Calculator

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Square Footage Calculator

Find the square footage of an area by selecting a shape and entering the dimensions. Include the price per sq ft to estimate the total cost.

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Area in Square Feet:
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Room/Area {{$index+1}} Square Feet

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How to Calculate Square Footage

Square footage is just an area measured in feet, and it’s often abbreviated sq ft or ft2. One square foot is equal to a square area with a length and width of 1 foot, or 12 inches.

Square footage is commonly used for construction, home remodeling, and renovation projects such as carpeting, hardwood flooring, tiling, drywalling, painting, and gardening material estimates.

You can calculate the square footage of a space using the area formula, which states that the area of a space is equal to its length times its width. This is the formula for a rectangle, but we’ll cover the area formulas for different shapes below.

Note that to calculate the area in square feet, the length and width must have units of feet. If they are in different units, then before you multiply them together, make sure to convert each measurement into feet.

For example, to calculate the square footage using measurements in inches or another measurement, first convert the length and width measurements to feet by dividing by 12, then multiply them together.

Steps to Calculate Square Feet

Find the area of a rectangular room or space in square feet by following these easy steps:

  • Measure the length and width of the area.
  • Convert these measurements to feet if they aren’t already. Convert inches, yards, or meters to feet using a converter if needed.
  • Multiply the length in feet times the width in feet (length × width). Use one of the formulas below to calculate square footage for various non-rectangular shapes.
  • To estimate the cost of materials to cover the area, multiply the total square footage by the price per square foot.
  • If the area is not a simple shape, break it into manageable parts and calculate the area of each part separately and then add them together. For example, to measure a floor of your home, calculate the square feet of each room, then add all area measurements together to derive the total square footage.

Square Footage Formulas

Use the formulas below to find the area in square feet for various shapes. Convert all measurements to feet before using the formulas.

Rectangle

sq ft = l × w

l = length
w = width

Rectangular Border

sq ft = (l × w) – (a × b)

l = outer length
w = outer width
a = inner length
b = inner width

Circle

sq ft = πr2

r = radius
π = 3.14159265359

If you know the diameter of the circle, you can find the radius by dividing the diameter in half.

Triangle

sq ft = bh/2

b = base
h = height

If you don’t know the height of the triangle, you can find it using the length of the three sides.

s = 1/2(a + b + c)

sq ft =√s(s – a)(s – b)(s – c)

a = edge a
b = edge b
c = edge c

How to Find the Square Footage of a Room

You can use the formulas above to find the square footage of any room in your home. Measure the dimensions of the room using a tape measure, then apply them to the applicable formula.

For instance, if the room is rectangular, measure the length and width in feet. Then, multiply them together to find the area in square feet.

For oddly shaped rooms, split the room into smaller, easily measurable sections, and calculate the area of each section separately. Add the area of each section together to find the total square footage of the room.

How to Calculate the Square Feet of a Home or Residence

As noted above, measuring the square footage of a house is important in real estate and for home improvements. Unlike measurements for a flooring project, when you’re measuring the area of a home or residence for real estate purposes, some special considerations apply to determine the inhabitable square footage.

Since the livable size of a home determines the market value, appraisal price, and property taxes, getting an accurate measurement is important.

Only livable rooms with finished walls, floor, and ceiling count toward the finished area of the home. For a room to be considered livable, the space should be finished and should have heating or air conditioning as applicable.

Indoor spaces like bedrooms and closets count toward the square footage of a home, while outdoor spaces such as a balcony or garage typically do not. In fact, the American National Standards Institute has defined rules[1] for what counts as a finished area and which rooms contribute to the gross living area (GLA) of a home.[2]

To calculate the total square footage of a home, measure each room in feet using a tape measure. Then, for each room, calculate the area using the appropriate formula depending on its shape.

Finally, add the area measurements together to find the total square footage. The calculator above can help find the square footage of one or more rooms using this method.

We also have great resources on how to measure rooms and complex spaces.

How to Calculate Price per Sq Ft

To calculate the price per square foot of your home, divide the total price of the home by the total number of square feet.

price per ft2 = total price ÷ total ft2

If you’d prefer not to do the math, you can also use our unit price calculator to calculate the price per square foot.

How to Convert to Square Feet

You can also calculate square feet by converting a known area that’s in different units of measure. You can convert square inches, square yards, or square meters to square feet using one of the formulas below.

Square Inches:

sq ft = sq in ÷ 144

Square Yards:

sq ft = sq yds × 9

Square Meters:

sq ft = sq m × 10.764

You can use an area converter to convert any area measurement to sq ft.

Frequently Asked Questions

No, feet are a one-dimensional unit of length, while square feet are a two-dimensional unit of area

One square foot is equal to the space taken up by a 1 ft by 1 ft square. You can visualize this by making a square out of 4 standard 12-inch rulers.

Square feet are used any time you want to represent the area of a space. It is most commonly used in measuring the living space of homes, but is also commonly used in landscaping and commercial real estate.

A 12 ft by 12 ft room is equal to 144 sq ft:
12 ft × 12 ft = 144 sq ft

Square Feet to Cubic Yards Calculator

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Square Feet to Cubic Yards Calculator

Convert square feet to cubic feet or vice-versa using the calculator below. Read on to learn how we calculated the result.

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Square Feet to Cubic Yards

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Cubic Yards to Square Feet

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How to Convert Square Feet to Cubic Yards

To calculate cubic yards given an area in square feet, you’ll also need the height or depth of the space/object in question. This is because these are different units of measure, so to convert one from the other, you need the height.

Square feet measure the area of a space, while cubic yards measure its volume.To convert, you can use a formula.

Square Feet to Cubic Yards Formula

The formula to convert is (for a rectangular or cubic volume only):

cu yds = sq ft × heightft ÷ 27

Thus, the volume of a space in cubic yards is equal to the area of the base in square feet times the height in feet, divided by 27. Essentially, you’re calculating the volume in cubic feet, then by dividing by 27, you’re converting the result to cubic yards.

If you don’t know the square footage, you can always use our square footage calculator, or if you know the length and width of the space, you can use this formula:

cu yds = (length ft × width ft × height ft) ÷ 27

Steps to Convert

Now that you know the conversion formula, follow these steps to convert square feet to cubic yards.

Step one: calculate the square footage of the space by multiplying the length and width.
Step two: calculate the cubic footage of the space by multiplying the square footage by the height or depth in feet.
Step three: calculate the cubic yardage of the space by dividing the cubic footage by 27. You can also use a cubic yards calculator for this

How to Convert Cubic Yards to Square Feet

You can convert cubic yards back to square feet by reversing the steps above. Of course, you’ll need to know the conversion formula.

Cubic Yards to Square Feet Formula

Use this formula to calculate square feet given cubic yards:

sq ft = (cu yds × 27) ÷ heightft

The area in square feet is equal to the volume in cubic yards times 27, divided by the height in feet.

You might also be interested in our square feet to cubic feet calculator.

Frequently Asked Questions

Cubic yards is a measurement of volume, while square yards is a measurement of area. That is, cubic yards are three-dimensional, while square yards are two-dimensional.

Square feet is a measure of area, whereas a cubic yard is a measure of volume, so we cannot provide a tangible answer to this question without knowing a little more about the area. A 3′ x 3′ area that is 3′ high will be equivalent to one cubic yard.

This depends on the desired depth of concrete over the specified area. For example, if we desire a depth of 6 inches of concrete, then a cubic yard of concrete would cover 54 square feet.

You can calculate this more specifically using our concrete calculator.

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Scale Conversion Calculator

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Scale Conversion Calculator

Scale a measurement to a larger or smaller measurement, which is useful for architecture, modeling, and other projects. You can also add the real size and scaled size to find the scale factor.

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How to Scale a Measurement

Making a measurement smaller or larger, known as scale conversion, requires a common scale factor, which you can use to multiply or divide all measurements.

To scale a measurement down to a smaller value, for instance, when making a blueprint, simply divide the real measurement by the scale factor. The scale factor is commonly expressed as 1:n or 1/n, where n is the factor.

For example, if the scale factor is 1:8 and the real measurement is 32, divide 32 ÷ 8 = 4 to convert.

To convert a smaller, scaled measurement up to the actual measurement, simply multiply the scaled measurement by the scale factor. For example, if the scale factor is 1:8 and the scaled length is 4, multiply 4 × 8 = 32 to convert it to the larger actual size.

A common tool used to scale a measurement from a real-world measurement is an architect’s scale rule. These are often used for scaling drawings and blueprints for buildings.

There are also engineering rules that are primarily used in civil engineering to scale measurements for roadways and land development. For example, when creating detail drawings, a scale of 1:10 is often used, and when creating working plans, scales of 1:20 or 1:40 are the preferred choices.

How to Find the Scale Factor

A scale factor is a ratio of two corresponding measurements or lengths. You can use the factor to increase or decrease the dimensions of a geometric shape, drawing, or model to different sizes. You can find the scale factor in a few easy steps.

Step One: Use the Scale Factor Formula

Since the scale factor is a ratio, the first step to finding it is to use the following formula:

scale factor =
scaled size
real size

So, the scale factor is a ratio of the scaled size to the real size.

Step Two: Simplify the Fraction

The next step is to reduce or simplify the fraction.

If you’re scaling down, that is, if the scaled size is smaller than the actual size, then the ratio should be shown with a numerator of 1. If you’re scaling up, that is, if the scaled size is larger than the actual size, then the ratio should be shown with a denominator of 1.

To find the final scale factor when you’re scaling up, reduce the ratio to a fraction with a denominator 1. To do this, divide both the numerator and the denominator by the denominator.

Note: by doing this, the numerator may become a decimal. This may or may not be desired, depending on your use case. If it’s not desired, then simply reduce the fraction like you would normally.

If you’re scaling down, then reduce the fraction so that the numerator is 1. You can do this by dividing both the numerator and the denominator by the numerator. Again, this may not result in whole numbers, so adjust accordingly.

Our fraction simplifier can help with this step if needed.

Step Three: Rewrite the Fraction as a Ratio

Finally, rewrite the fraction as a ratio by replacing the fraction bar with a colon. For instance, a scale factor of 1/10 can be rewritten as 1:10.

For example, let’s find the scale factor used on an architectural drawing where ½” on the drawing represents 12″ on the final building.

Begin by replacing the values in the formula above.

scale factor =
½”
12″

Since the drawing is scaled down, then the scale factor should be reduced to a fraction with a numerator of 1.

Multiply both the numerator and denominator by 2 to simplify.

scale factor =
½” × 2
12″ × 2
= 1/24

And finally, rewrite the fraction as a ratio.

Thus the scale factor for this drawing is 1:24.

scale factor =
1
24
= 1.24
How to Reduce the Scale Factor

If you already know the scale factor, but it is not in the form of 1:n or 1/n, then some additional work is needed to reduce or simplify it. If the ratio is 2:3, for example, then you’ll need to reduce it so that the numerator is 1.

Use our ratio calculator to reduce a ratio. You can also reduce a ratio by dividing both the numerator and the denominator by the numerator.
For example: reduce 2/3 by dividing both numbers by 2, which would be 1/1.5 or 1:1.5.

2 ÷ 2 = 1
3 ÷ 2 = 1.5
scale factor = 1:1.5

Architectural Scales

Architectural scales often relate a measurement, in feet, of a building to inches on a drawing. You can quickly find the scale factor for an architectural scale by inverting the fraction, then multiplying it by 12 (inches/foot).

For example, to find the scale factor on a drawing equaling 1′ on a building (1/16″ = 1′), start by inverting the fraction 1/16 so that it becomes 16/1. Then, multiply that by 12, which is 192. So, the scale factor for 1/16″ = 1′ is 1:192.

Scale factors for common architectural scales

Drawing Scale Scale Factor
1/16″ = 1′ 1:192
3/32″ = 1′ 1:128
1/8″ = 1′ 1:96
3/16″ = 1′ 1:64
1/4″ = 1′ 1:48
3/8″ = 1′ 1:32
1/2″ = 1′ 1:24
3/4″ = 1′ 1:16
1″ = 1′ 1:12
1 1/2″ = 1′ 1:8
3″ = 1′ 1:4
Engineering Scales

Engineering scales are represented in the same units for both the drawing and the actual measurement. For example, if you have a ratio of inches on a drawing to feet in reality, you can quickly find the scale factor for an engineering, or civic, scale by multiplying the feet portion by 12 (inches/foot).

As an example, to find the scale factor for 1″ = 30′, multiply 30′ by 12, which is 360. So, the scale factor for 1″ = 30′ is 1:360.

Scale factors for common engineering scales

Drawing Scale Scale Factor
1″ = 10′ 1:120
1″ = 20′ 1:240
1″ = 30′ 1:360
1″ = 40′ 1:480
1″ = 50′ 1:600
1″ = 60′ 1:720
1″ = 70′ 1:840
1″ = 80′ 1:960
1″ = 90′ 1:1080
1″ = 100′ 1:1200

Common Model Scales

This table lists some common scale factors you may come across when dealing with different types of models.

Scale Factor Model Type
1:4 steam trains, RC planes
1:8 steam trains, cars
1:10 figures
1:12 cars, motorcycles, dollhouses
1:16 steam trains, cars, motorcycles, military vehicles, figures
1:18 diecast cars
1:20 formula one cars
1:22.5 G-gauge trains
1:24 cars, trucks, aircraft, dollhouses
1:25 cars, trucks
1:32 1 gauge trains, cars, aircraft, figures
1:35 military vehicles
1:43 O-gauge trains, cars, trucks
1:48 O-gauge trains, dollhouses, Lego minifig
1:64 S-gauge trains, diecast cars, Hotwheels/Matchbox
1:72 aircraft, military vehicles, boats, cars
1:76 aircraft, military vehicles
1:87 HO-gauge trains, military vehicles
1:96 ships, spacecraft
1:100 aircraft, spacecraft
1:120 TT-gauge trains
1:144 ships, rockets, spacecraft
1:160 N-gauge trains, wargaming
1:200 aircraft, ships
1:220 Z-gauge trains
1:285 wargaming
1:350 ships
1:700 ships
1:720 ships

Common scale factors used for models and hobbies

Frequently Asked Questions

Yes, the scale factor can be represented as a fraction that describes the relative size between a model or drawing, and the actual object.

No, the scale factor is not always greater than one. It will be greater than one if the model is smaller than the actual object, but smaller than one if the model is larger than the actual object.

Typically we make models that are smaller than the object being modeled, hence why the scale factor is usually greater than one.

You can calculate scale from a drawing by measuring what length on the drawing corresponds to what length on the actual object. For example, if 1 inch on the drawing equals 3 inches on the actual object, then the scale is 1:3.

An example of a scale factor is the ratio used on a model airplane to describe how much bigger the actual airplane is than the model. If the actual airplane is ten times bigger than the model, then the scale factor is 1:10.

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Inch Fraction Calculator

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Inch Fraction Calculator

Convert inch fractions to decimal, decimal to inches, inches to metric measurements, metric measurements to inch fractions, and inches to feet using our inches to fraction calculator.

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How to Calculate Inch Fractions

Measurements in inches can be expressed as a decimal or a fraction. When inches are expressed as a fraction, there are some special rules to follow, which are important to know to convert a decimal to inches correctly.

While fractions of an inch can be represented as any standard fraction, the most common fractions of an inch use denominators that are powers of 2, from half inches to up to the 64ths of an inch. That means the fraction denominators are most commonly 2, 4, 8, 16, 32, and 64.

These specific fractions of an inch are referred to as inch fractions.

As a result, if we want to convert a decimal to one of these inch fractions, then know that converting a decimal to an inch fraction is not quite the same as converting a decimal to a regular fraction.

Instead, some minor rounding will occur since it will be necessary to find the nearest fraction with the denominator that is a power of 2, also known as a dyadic fraction or dyadic rational number.[1] Typical inch fractions will look something like 1/64, 1/32, 1/16, 1/8, 1/4, or 1/2.

When you’re working with larger measurements, you can use our feet and inches calculator to add or subtract feet and inch fractions.

How to Convert Inches to Fraction

To convert decimal inches to an inch fraction, you’ll need to round the decimal portion to the nearest dyadic fractional inch.

First, separate the whole number from the decimal; these are the whole inches. Then, take the remaining portion of the decimal to the right of the decimal point and multiply it by the denominator of the level of precision you need (e.g., 1/16, 1/32, or 1/64).

For instance, to round to the nearest 1/16, take the decimal portion and multiply it by 16. Then, round the result to get the numerator of the inch fraction.

Finally, place the numerator over the level of precision, 16 in this case. Then, put the fractional inches next to the whole inches for the final result.

For example, let’s convert 2.695 inches to a fraction with 1/16″ precision.

Remove the whole number 2 from the decimal to leave us with the decimal 0.695.

Then, multiply 0.695 by 16.

0.695 × 16 = 11.12

Round this to the nearest whole number; in this case, 11.12 can be rounded to 11. Put that in a fraction over 16, so 11/16 is the remaining inch fraction.

Put it all together by placing the whole inches (2) in front of the inch fraction.

2.695 in ≈ 2 11/16

Thus, using this method, you can see that 2.695 decimal inches are approximately equal to 2 11/16 as an inch fraction. Note that we use an “approximately equal” sign instead of an equals sign because the two numbers are not exactly equal.

Decimal to Inches Chart

Use this decimal to inches chart to easily find the correct fraction for your decimal measurement or to convert inches to fraction. Find decimal equivalents in 1⁄64” increments, including 1⁄2“, 1⁄4“, 1⁄8“, 1⁄16“, and 1⁄32” measurements.

The chart also shows hints on the markings sizes found on a tape measure or ruler.

How to Convert Inch Fractions to Decimal

Converting an inch fraction to decimal inches is as easy as dividing the fraction. Divide the top number (numerator) by the bottom number (denominator) to find the value in inches as a decimal.

You can also use a fraction to decimal calculator or the chart below.

Inches to Decimal Chart

The inch fraction to decimal and metric chart below shows equivalent length measurements in fraction, decimal, and millimeters up to one inch in 1⁄64” increments. You can use this to convert inches to decimal or millimeters.

Fraction
(inches)		 Decimal
(inches)		 Metric
(millimeters)
1/64″ 0.015625″ 0.396875 mm
1/32″ 0.03125″ 0.79375 mm
3/64″ 0.046875″ 1.190625 mm
1/16″ 0.0625″ 1.5875 mm
5/64″ 0.078125″ 1.984375 mm
3/32″ 0.09375″ 2.38125 mm
7/64″ 0.109375″ 2.778125 mm
1/8″ 0.125″ 3.175 mm
9/64″ 0.140625″ 3.571875 mm
5/32″ 0.15625″ 3.96875 mm
11/64″ 0.171875″ 4.365625 mm
3/16″ 0.1875″ 4.7625 mm
13/64″ 0.203125″ 5.159375 mm
7/32″ 0.21875″ 5.55625 mm
15/64″ 0.234375″ 5.953125 mm
1/4″ 0.25″ 6.35 mm
17/64″ 0.265625″ 6.746875 mm
9/32″ 0.28125″ 7.14375 mm
19/64″ 0.296875 7.540625 mm
5/16″ 0.3125″ 7.9375 mm
21/64″ 0.328125″ 8.334375 mm
11/32″ 0.34375″ 8.73125 mm
23/64″ 0.359375″ 9.128125 mm
3/8″ 0.375″ 9.525 mm
25/64″ 0.390625″ 9.921875 mm
13/32″ 0.40625″ 10.31875 mm
27/64″ 0.421875″ 10.715625 mm
7/16″ 0.4375″ 11.1125 mm
29/64″ 0.453125″ 11.509375 mm
15/32″ 0.46875″ 11.90625 mm
31/64″ 0.484375″ 12.303125 mm
1/2″ 0.5″ 12.7 mm
33/64″ 0.515625″ 13.096875 mm
17/32″ 0.53125″ 13.49375 mm
35/64″ 0.546875″ 13.890625 mm
9/16″ 0.5625″ 14.2875 mm
37/64″ 0.578125″ 14.684375 mm
19/32″ 0.59375″ 15.08125 mm
39/64″ 0.609375″ 15.478125 mm
5/8″ 0.625″ 15.875 mm
41/64″ 0.640625″ 16.271875 mm
21/32″ 0.65625″ 16.66875 mm
43/64″ 0.671875″ 17.065625 mm
11/16″ 0.6875″ 17.4625 mm
45/64″ 0.703125″ 17.859375 mm
23/32″ 0.71875″ 18.25625 mm
47/64″ 0.734375″ 18.653125 mm
3/4″ 0.75″ 19.05 mm
49/64″ 0.765625″ 19.446875 mm
25/32″ 0.78125″ 19.84375 mm
51/64″ 0.796875″ 20.240625 mm
13/16″ 0.8125″ 20.6375 mm
53/64″ 0.828125″ 21.034375 mm
27/32″ 0.84375″ 21.43125 mm
55/64″ 0.859375″ 21.828125 mm
7/8″ 0.875″ 22.225 mm
57/64″ 0.890625″ 22.621875 mm
29/32″ 0.90625″ 23.01875 mm
59/64″ 0.921875″ 23.415625 mm
15/16″ 0.9375″ 23.8125 mm
61/64″ 0.953125″ 24.209375 mm
31/32″ 0.96875″ 24.60625 mm
63/64″ 0.984375″ 25.003125 mm
1″ 1.0″ 25.4 mm

Inch fractions to the 1/64 of an inch and the equivalent decimal values in inches and metric values in millimeters

How to Convert Inches to Metric Measurements

To convert inch fractions to metric measurements, you need to keep in mind that there are 2.54 centimeters or 25.4 millimeters per inch.

So, to convert an inch fraction to centimeters, you multiply the inches by 2.54, and to convert to millimeters, multiply by 25.4.

cm = in × 2.54
mm = in × 25.4
You can also use a length converter such as an SAE to metric converter.

How to Find Inch Fractions on a Tape Measure

Finding measurements on a ruler or tape measure can be confusing at first, but once you understand how the marks are laid out, then you’ll see it is quite simple. Notice that the markings between the whole-inch numbers vary in length.

The longest markings will be the quarter-inch markings, i.e., the first marking is 1/4 inch, the second is 1/2 (2/4) inch, and the third is 3/4 inch.

The next longest markings will be the eighth-inch markings, i.e., the first marking is 1/8 inch, the second is 3/8 inch, the third is 5/8 inch, etc.

The smallest markings will be the sixteenth-inch markings, i.e., the first marking is 1/16 inch, the second is 3/16 inch, the third is 5/16 inch, etc.

We also have a free printable ruler with fraction measurements marked to help you learn how to find the inch fractions for a measurement. If you need measurements more precise than 64ths of an inch, then you will need to use a more accurate measuring tool such as calipers.

Frequently Asked Questions

An inch fraction is a fraction of an inch with a denominator that is a power of two. For example, 1/2, 3/8, 15/16, 17/32, and 33/64 are all examples of inch fractions.

If you are more familiar with the metric system, one inch is equal to 25.4 millimeters or 2.54 centimeters. If not, a standard paperclip is one inch long, and the diameter of a U.S. quarter is also approximately one inch.

You can use either decimals or fractions when representing portions of an inch. Typically we use fractions when the portion of an inch equals one of the common inch fractions in the list above.

The U.S. uses inches because it abides by the imperial system of measurements, whereas most of the rest of the world uses the metric system.

The United Kingdom adopted these imperial units in 1826, and since, at the time, it had much influence in the United States, the U.S. adopted them as well. Today, however, the United Kingdom has changed to primarily use the metric system.

Inches are usually represented either with the abbreviation in, or with a double apostrophe, known as a double prime, ″. For example:

5 inches = 5 in = 5″

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Feet and Inches Length Calculator

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Feet and Inches Length Calculator

Add or subtract lengths in inches (decimal or fraction), feet, centimeters, and millimeters. Enter equations just like you would write it on paper, e.g. 4′ 3 7/8″ + 5 cm.

See the results in inches, feet, centimeters, and millimeters – all results are in imperial and metric.

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How to Add or Subtract Feet and Inches

Calculating feet and inches might seem complicated, but adding and subtracting measurements is actually really easy if you follow a few simple steps. While it’s easy to add or subtract feet and inches using a measurement calculator like the one above, if you follow a few basic steps, you can do it yourself!

Step One: Convert Feet and Inches to Decimal

The first thing to do when adding, subtracting, or doing other math with inches, feet, and other measurements is to convert all the measurements into a common unit of measure. For example, when reading a tape measure, inches will be in fraction form.

Let’s assume we want to perform a calculation using inches as our unit of measurement. Start by converting any fractional inches into decimals. Then convert any measurements in feet, centimeters, millimeters, etc. to inches.

Convert any inch fractions to decimal form by dividing the numerator of the fraction by the denominator, using a calculator if necessary. If there is a whole number associated with the fraction, add it to the decimal value after converting.

For example, if our measurement is 2 and 1/2 inches, first convert 1/2 to a decimal, which is 0.5, and then add it to 2, for a total of 2.5 inches.

You can also use an inch fraction calculator to quickly find the decimal value for an inch fraction.

For example:

3/8 = 3 ÷ 8 = .375 inches

Convert any feet to inches by multiplying the number of feet by 12, since there are 12 inches in a foot. Using a foot to inch conversion calculator also simplifies this step.

For example:

3 feet = 3 × 12 = 36 inches

Step Two: Add or Subtract the Converted Values

With all your measurements now in an inch decimal form, add or subtract them as you normally would, using a calculator as needed. The final result will be the length in inches; you can convert the result to any other unit at this point.

To express the sum or difference value in feet, simply divide by 12.

The following charts simplify the process of adding and subtracting fractional inch values together and might be faster than using a calculator.

Inch Fraction Addition Chart

Table showing the sum of common inch fractions. Add a fraction from the top heading and first column; the sum is where they intersect.

+ 1/8″ + 1/4″ + 3/8″ + 1/2″ + 5/8″ + 3/4″ + 7/8″ + 1″
1/8″ 1/4″ 3/8″ 1/2″ 5/8″ 3/4″ 7/8″ 1″ 1 1/8″
1/4″ 3/8″ 1/2″ 5/8″ 3/4″ 7/8″ 1″ 1 1/8″ 1 1/4″
3/8″ 1/2″ 5/8″ 3/4″ 7/8″ 1″ 1 1/8″ 1 1/4″ 1 3/8″
1/2″ 5/8″ 3/4″ 7/8″ 1″ 1 1/8″ 1 1/4″ 1 3/8″ 1 1/2″
5/8″ 3/4″ 7/8″ 1″ 1 1/8″ 1 1/4″ 1 3/8″ 1 1/2″ 1 5/8″
3/4″ 7/8″ 1″ 1 1/8″ 1 1/4″ 1 3/8″ 1 1/2″ 1 5/8″ 1 3/4″
7/8″ 1″ 1 1/8″ 1 1/4″ 1 3/8″ 1 1/2″ 1 5/8″ 1 3/4″ 1 7/8″
1″ 1 1/8″ 1 1/4″ 1 3/8″ 1 1/2″ 1 5/8″ 1 3/4″ 1 7/8″ 2″
Inch Fraction Subtraction Chart

Table showing the difference of common inch fractions. Subtract a fraction from the top heading from the first column; the difference is where they intersect.

− 1/8″ − 1/4″ − 3/8″ − 1/2″ − 5/8″ − 3/4″ − 7/8″ − 1″
1/8″ 0″ -1/8″ -1/4″ -3/8″ -1/2″ -5/8″ -3/4″ -7/8″
1/4″ 1/8″ 0″ -1/8″ -1/4″ -3/8″ -1/2″ -5/8″ -3/4″
3/8″ 1/4″ 1/8″ 0″ -1/8″ -1/4″ -3/8″ -1/2″ -5/8″
1/2″ 3/8″ 1/4″ 1/8″ 0″ -1/8″ -1/4″ -3/8″ -1/2″
5/8″ 1/2″ 3/8″ 1/4″ 1/8″ 0″ -1/8″ -1/4″ -3/8″
3/4″ 5/8″ 1/2″ 3/8″ 1/4″ 1/8″ 0″ -1/8″ -1/4″
7/8″ 3/4″ 5/8″ 1/2″ 3/8″ 1/4″ 1/8″ 0″ -1/8″
1″ 7/8″ 3/4″ 5/8″ 1/2″ 3/8″ 1/4″ 1/8″ 0″

We’ve covered the basics of adding length measurements, and we hope you’re feeling confident using the steps above. Learn more about how to add feet and inches with our in-depth guide.

How to Multiply or Divide Feet & Inches

The steps to multiply or divide feet and inches are similar to the steps for adding and subtracting above.

The first step in multiplying or dividing multiple measurements together is to convert the length measurements to the same unit of measurement and then to convert them to a decimal value. If the length measurements are in feet and inches, it might be easiest to convert to inches.

Step One: Convert Feet and Inches to Decimal

The first step in multiplying or dividing multiple measurements together is to convert the length measurements to the same unit of measurement and then to convert them to a decimal value. If the length measurements are in feet and inches, it might be easiest to convert to inches.

Step Two: Multiply or Divide

With the length values converted to a decimal, it’s now possible to multiply or divide just like you would with any decimal number. For example, if your inch value is 1.25 and you need to multiply by 2, simply multiply using 1.25 × 2 = 2.5.

If you need to multiply two measurements together, for instance, to calculate an area, then be sure to update the units to square units. For example, 2.5 in × 4 in = 10 in2.

The following charts make multiplying or dividing fractional inch values much easier.

Inch Fraction Multiplication Chart

Table showing the multiplication of common inch fractions. Multiply the fraction in the first column by the top heading’s value; the result is where they intersect.

× 2 × 3 × 4 × 5 × 6 × 7 × 8
1/8″ 1/4″ 3/8″ 1/2″ 5/8″ 3/4″ 7/8″ 1″
1/4″ 1/2″ 3/4″ 1″ 1 1/4″ 1 1/2″ 1 3/4″ 2″
3/8″ 3/4″ 1 1/8″ 1 1/2″ 1 7/8″ 2 1/4″ 2 5/8″ 3″
1/2″ 1″ 1 1/2″ 2″ 2 1/2″ 3″ 3 1/2″ 4″
5/8″ 1 1/4″ 1 7/8″ 2 1/2″ 3 1/8″ 3 3/4″ 4 3/8″ 5″
3/4″ 1 1/2″ 2 1/4″ 3″ 3 3/4″ 4 1/2″ 5 1/4″ 6″
7/8″ 1 3/4″ 2 5/8″ 3 1/2″ 4 3/8″ 5 1/4″ 6 1/8″ 7″
1″ 2″ 3″ 4″ 5″ 6″ 7″ 8″
Inch Fraction Division Chart

Table showing the division of common inch fractions. Divide the fraction in the first column by the top heading’s value; the result is where they intersect.

÷ 2 ÷ 3 ÷ 4 ÷ 5 ÷ 6 ÷ 7 ÷ 8
1/4″ 1/8″ 5/64″ 1/16″ 3/64″ 1/32″ 1/32″ 1/64″
1/2″ 1/4″ 11/64″ 1/8″ 7/64″ 5/64″ 1/16″ 1/16″
3/4″ 3/8″ 1/4″ 3/16″ 5/32″ 1/8″ 7/64″ 3/32″
1″ 1/2″ 21/64″ 1/4″ 13/64″ 11/64″ 9/64″ 1/8″

Inch Fraction and Decimal Equivalents

Sometimes a chart makes things easier: find common inch fractions and equivalent decimal values using this one.

 

Frequently Asked Questions

Feet are represented as “ft.” or a single apostrophe, such as 5 ft. or 5′. Inches are represented as “in.” or a double apostrophe, such as 5 in. or 5″.

Yes, 12 inches are equivalent in length to 1 foot.

To calculate inches from feet manually, first, convert any fractional feet to a decimal and add it to the whole number of feet, then multiply the resulting value by 12.

For example, to convert 2 1/2 feet to inches:
2 1/2 ft = 2.5 ft = 30 in

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