Volume Calculator
Calculate the volume of a sphere, ellipsoid, cylinder, cone, cube, rectangular prism or pyramid. Enter the dimensions in one unit and the result comes back in that unit cubed.
How to use the Volume Calculator
- Enter your numbers in the Volume Calculator above.
- Press the Calculate Volume button to see the result.
- To try other numbers, change any value and press the button again.
Common volume formulas
Sphere: 4/3·π·r³ · · · Ellipsoid: 4/3·π·a·b·c · · · Cylinder: π·r²·h · · · Cone: 1/3·π·r²·h · · · Cube: s³ · · · Rectangular prism: l·w·h · · · Pyramid: 1/3·l·w·h
Each shape has its own formula. The calculator covers seven shapes and asks only for the dimensions that shape needs. An ellipsoid has three semi-axes, a, b and c, which are half its length, half its width and half its height. Make all three equal to r and the ellipsoid formula turns into the sphere formula. The pyramid stands on a rectangular base, so its volume is a third of the box with the same base and height. The calculator does not convert units. Measure every dimension in the same unit and read the answer in that unit cubed. Every field the shape shows needs a value of 0 or more. A volume below 0.0001 shows in scientific notation, such as 5.236 × 10^-7.
Worked example
A cylinder with radius 5 cm and height 10 cm: V = π × 5² × 10 = 250π ≈ 785.3982 cm³. A sphere of the same radius: V = (4/3)π × 5³ ≈ 523.5988 cm³, two thirds of the cylinder that encloses it. An ellipsoid with semi-axes of 5 cm, 4 cm and 3 cm: V = (4/3)π × 5 × 4 × 3 = 80π ≈ 251.3274 cm³, less than half that sphere. A pyramid with a 6 cm by 4 cm base and a height of 5 cm: V = 6 × 4 × 5 ÷ 3 = 40 cm³.
Frequently asked questions
What unit is the volume in?
The cube of the unit you measured in. Centimeters give cubic centimeters and feet give cubic feet. The calculator labels the result "units³" and leaves the unit to you. One cubic centimeter is one milliliter and one cubic meter is 1,000 liters. To turn liters into US gallons or quarts, use the conversion calculator.
How do I find the volume of an ellipsoid?
Pick Ellipsoid and enter the three semi-axes a, b and c. Each one is half the full width of the shape along that axis, so an ellipsoid 10 cm long and 6 cm across has semi-axes of 5, 3 and 3. The volume is 4/3 × π × a × b × c, which gives 60π ≈ 188.4956 cm³ for that shape. Enter the same number for all three and you get the volume of a sphere with that radius.
How do I find the volume of a pyramid?
Pick Pyramid, then enter the length and width of the base and the height from the base to the tip. The volume is length × width × height ÷ 3, so a 6 by 4 base with a height of 5 gives 40. The base is a rectangle. For a square pyramid, enter the same number for length and width.
What about irregular shapes?
Split the object into shapes the calculator knows and add up their volumes. A bottle, for example, is close to a cylinder with a cone on top. If the object fits in a container of water, you can also measure how far the water level rises when you sink it. The volume of water it pushes aside is its own volume.
What's the volume of a frustum?
A frustum is a cone or pyramid with the top cut off. The calculator has no frustum shape, so work it out by hand: V = (1/3)·h·(A₁ + A₂ + √(A₁·A₂)), where h is the height between the two parallel faces and A₁ and A₂ are their areas. A square pyramid frustum 6 by 6 at the bottom, 3 by 3 at the top and 4 high has A₁ = 36 and A₂ = 9, so V = (1/3) × 4 × (36 + 9 + 18) = 84.