Volume Calculator

Calculate volume by selecting one of the shapes below and entering your measurements in any unit.

Diagram of a rectangular prism showing l = length, w = width, and h = height

Volume:

 
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How to Find Volume

Volume is the measure of 3-dimensional space that a geometric shape or object occupies. It’s measured in cubic units, such as cubic yards or cubic feet.

Of course, you can find volume easily using a calculator like the one above, but you can also find it yourself using a formula. Read on to learn more about how to calculate it.

Volume Formulas

The volume of every shape is calculated differently using a different formula. Use the formulas below to find the volume of several three-dimensional shapes.

Formulas to find the volume for several shapes

Volume of a Cube

V = a3

a = edge a length

Diagram of a cube showing a = edge length

Volume of a Rectangular Prism

V = l × w × h

l = length
w = width
h = height

Diagram of a rectangular prism showing l = length, w = width, and h = height

Volume of a Sphere

V = 4 / 3πr3

r = radius

Diagram of a sphere showing r = radius

Volume of a Cylinder

V = πr2h

r = radius
h = height

Diagram of a cylinder showing r = radius and h = height

Volume of a Cone

V = 1 / 3πr2h

r = radius
h = height

Diagram of a cone showing r = radius and h = height

Volume of a Pyramid

V = 1 / 3e2h

e = edge length
h = height

Diagram of a pyramid showing e = edge length and h = height

Volume of a Triangular Prism

s = 1/2(a + b + c)
V = h × s(s – a)(s – b)(s – c))

a, b & c = triangle sides

h = height

Diagram of a triangular prism showing sides a, b, & c, and h = height

Volume of a Capsule

V = πr2h + 4 / 3πr3

r = radius
h = height

Diagram of a capsule showing r = radius and h = height

Volume of a Hemisphere

V = 2 / 3πr3

r = radius

Diagram of a hemisphere showing r = radius

Volume of a Spherical Cap

V = π / 6h(3r2 + h2)

r = radius
h = height

Diagram of a cap showing r = radius and h = height

How to Find the Volume of an Irregular Object

The formulas above can be used to calculate regular objects with a defined formula, but many objects are irregular or have no obvious formula. Water displacement is a technique used to find the amount of space an irregular object consumes.

The water displacement technique involves filling a container with water and measuring the amount of water displaced by submerging the irregular object in the water in the container.

For example, fill a container with water and calculate the volume of the water using the formulas above.

Submerge the irregular object in the water and observe that the water level in the container has risen.

Measure the amount of water as before and calculate the volume of the water with the object submerged.

Subtract the initial result by the result after the irregular object was placed in the water to find the volume of the object.

Measuring Volume Using Weight

In some cases, you can measure the volume of a fluid or irregular solid material by measuring its mass. If you know the density of the material, you can calculate the volume using its mass with the following formula:

V = m / ρ

where:
V = volume
m = mass
ρ = density

The volume of a material is equal to the mass m divided by its density ρ.

This technique is commonly used to estimate the volume of materials like gravel or water.

Volume Measurement Tips

One important consideration when measuring is to take all measurements using the same unit of measure. If your measurements are in different units, convert each measurement to the unit you want the results in.

Use our length converter to convert your measurements to a consistent unit. You can also use our volume converter to convert your result to another unit of measure.

Common Volume Measurements

Table showing common volume measurements in metric and imperial units
Cubic Inch Cubic Foot Cubic Yard Cubic Centimeter Cubic Meter
1 Cubic Inch = 1 in3 0.000579 ft3 0.000021434 yd3 16.3871 cm3 0.000016387 m3
1 Cubic Foot = 1,728 in3 1 ft3 0.037037 yd3 28,317 cm3 0.028317 m3
1 Cubic Yard = 46,656 in3 27.000049 ft3 1 yd3 764,555 cm3 0.764555 m3
1 Cubic Centimeter = 0.061024 in3 0.000035315 ft3 0.000001308 yd3 1 cm3 0.0000010 m3
1 Cubic Meter = 61,024 in3 35.314725 ft3 1.30795 yd3 1,000,000 cm3 1 m3

You might also be interested in our surface area calculator to find the surface area of a shape.