How to use the volume calculator
- Choose a shape: box, cube, cylinder, hollow cylinder, sphere, hemisphere, cone, cone frustum, rectangular pyramid, ellipsoid or capsule.
- Choose the length unit (inches, feet, yards, millimeters, centimeters or meters) and use it for every dimension.
- Enter the dimensions that appear for that shape. Radius is half the diameter.
- Read the volume in cubic units of your choice, plus cubic inches, feet, yards, meters, liters and US gallons.
Formula
Box: V = length x width x height. Cube: V = side^3
Cylinder: V = pi r^2 h. Hollow cylinder: V = pi (R^2 - r^2) h
Sphere: V = 4/3 pi r^3. Hemisphere: V = 2/3 pi r^3
Cone: V = 1/3 pi r^2 h. Frustum: V = 1/3 pi h (R^2 + R r + r^2)
Rectangular pyramid: V = 1/3 x length x width x height. Ellipsoid: V = 4/3 pi a b c
Capsule: V = pi r^2 h + 4/3 pi r^3
Unit conversions use exact definitions: 1 in = 0.0254 m, 1 ft = 0.3048 m, 1 yd = 0.9144 m, 1 US gallon = 231 cubic inches and 1 cubic meter = 1,000 liters. Pi is the double-precision value.
Worked example
A box that is 10 ft long, 4 ft wide and 3 ft high has a volume of 120 cubic feet. That is 207,360 cubic inches, 4.4444 cubic yards, 3,398.0216 liters and 897.6623 US gallons.
A cylinder with radius 2 ft and height 3 ft holds pi x 4 x 3 = 37.699112 cubic ft. A sphere with radius 3 holds 4/3 x pi x 27 = 113.097336, and a cone with radius 3 and height 4 holds the same 37.699112 as that cylinder, one third of pi x 9 x 4 = 12 pi.
A cube with 1 meter sides holds 1,000 liters, which is 264.1721 US gallons.
Which dimensions to enter
Each shape asks only for what it needs, and the help text on each field explains the exceptions.
- A hollow cylinder (tube) uses an outer radius, an inner radius and a height. The inner radius must be smaller than the outer.
- A cone frustum uses a bottom radius, a top radius and a height. A top radius of 0 makes a full cone.
- An ellipsoid uses three semi-axes, which are half of each full width.
- A capsule uses the radius and the height of the straight middle part, not counting the two rounded ends.
Volume versus capacity
Volume is the space a shape occupies. Capacity is how much liquid a container holds, and it can be smaller because of wall thickness. For a container with thick walls, use the inside dimensions. For pools, tanks and concrete, you might also want the pool volume calculator or the concrete calculator, which include practical allowances.
Units and conversions
Enter all dimensions in the same unit. Surface-area problems use the area calculator, and general conversions use the unit converter. Results are rounded half up to the decimals shown, and gallons are US liquid gallons.
Assumptions and limits
- All dimensions use one length unit and must be positive numbers up to 100,000,000.
- Shapes are treated as solid, ideal geometric shapes. Rounded corners, wall thickness and tapering you do not enter are not modeled.
- Gallons are US liquid gallons (231 cubic inches). Imperial gallons are not shown.
- A frustum may have a top radius of 0, but every other dimension must be greater than 0.
- Everything runs in your browser. Nothing you enter is sent anywhere.
Frequently asked questions
How do I calculate the volume of a cylinder?
Multiply pi by the radius squared and then by the height. A cylinder with radius 2 ft and height 3 ft has a volume of about 37.7 cubic feet.
How many gallons are in a cubic foot?
A US liquid gallon is 231 cubic inches and a cubic foot is 1,728 cubic inches, so a cubic foot holds about 7.4805 gallons. The calculator applies that conversion for you.
What is the difference between a cone and a frustum?
A cone comes to a point. A frustum is a cone with the top cut off, so it has a second, smaller radius at the top. Enter a top radius of 0 to get a cone.
Why is a cone one third of a cylinder?
A cone with the same base and height as a cylinder fills exactly one third of it. The same one-third rule applies to a pyramid compared with a prism of the same base and height.
Can I enter the diameter instead of the radius?
Enter half the diameter. The field is labeled radius, so divide any diameter by 2 before typing it in.