Volume calculator
Pick a solid, enter its sizes, get the volume instantly.
How do I find the volume of a box?
Multiply length × width × height: a box 2 × 3 × 4 ft holds 24 cubic feet. For a cube, multiply the side by itself three times.
How do I find the volume of a cylinder?
π × radius² × height. A cylinder with a 2 ft radius and 5 ft tall holds 3.1416 × 4 × 5 = 62.83 cubic feet. A cone with the same base and height holds a third of that, 20.94.
How do I find the volume of a sphere?
4/3 × π × radius³. A ball with a 3 in radius holds 4/3 × 3.1416 × 27 = 113.1 cubic inches, or about 0.49 US gallons.
How do I find the volume of a pyramid?
A third of the base area times the height. A pyramid with a 6 × 6 base, 4 tall, is 6 × 6 × 4 ÷ 3 = 48.
How do I convert cubic feet to gallons or liters?
One cubic foot is 7.48 US gallons or 28.3 liters. Pick a unit and the table under the result shows the volume in the others, including gallons and liters.
How is a sphere related to the cylinder around it?
A sphere takes up two thirds of the cylinder that just contains it. With a radius of 3, the sphere's volume is 113.1 and the enclosing cylinder (radius 3, height 6) is 169.6; 113.1 ÷ 169.6 = 0.667. The cone with the same base and height as the cylinder is exactly one third of it, 56.5.
How many gallons are in a cubic foot, and how many liters?
A cubic foot is 1,728 cubic inches, and a US gallon is 231 cubic inches, so a cubic foot is 7.481 gallons. It is also 28.32 liters (exactly, because a foot is 0.3048 meter and a liter is a thousandth of a cubic meter). A cylinder 2 ft across and 3 ft tall, with a radius of 1 ft, holds 9.42 cubic feet, or 70.5 gallons.
The formulas
Volume is the amount of space an object takes up. For a box it is length × width × height; a cube is the side cubed. A cylinder is the area of the circle, π r², times the height. A cone and a pyramid are each one third of the cylinder or prism with the same base and height. A sphere is 4/3 π r³ and a hemisphere half of that. A capsule, a cylinder with a hemisphere at each end, is π r² h + 4/3 π r³, where h is the length of the straight part only. All dimensions must be in the same unit, and the result is in that unit cubed. The calculator can then show it in cubic feet, gallons and liters.
Worked example: five shapes with a radius of 3
A sphere with a radius of 3 has a volume of 4/3 × π × 27 = 113.1. A cylinder of radius 3 and height 6 has π × 9 × 6 = 169.6; a cone with the same base and height has 56.5. A pyramid with a 6 × 6 base and a height of 4 has 6 × 6 × 4 ÷ 3 = 48, one third of the 144 of the box around it. A capsule with a radius of 1 and a straight section of 4 has π × 4 + 4/3 π = 16.76. For lengths in inches these are cubic inches, which you can divide by 231 for US gallons.
Volume, capacity and weight
Volume describes the outside dimensions; the capacity of a container is the volume inside, so subtract the wall thickness. To get weight you multiply the volume by the density of the material, for which you need a table value for the material. The calculator on this page gives volume only; the concrete, soil and water pages of this site add the density and the unit for the material, such as cubic yards, which is the unit in which many bulk materials are sold (one cubic yard is 27 cubic feet).
Common mistakes
Using the diameter in place of the radius is the most common error, and for a sphere it makes the result eight times too large: a ball with a radius of 3 has a volume of 113.1, but entering 6 gives 904.8. Mixing units is the second; to convert cubic feet to cubic inches multiply by 1,728 (12³), not by 12. Third, using the slanted side of a cone or a pyramid in place of the vertical height. And a hollow object, such as a pipe, needs the volume of the outer shape minus the volume of the hole.
Sources: volume formulas for the prism, cylinder, cone, pyramid and sphere as in OpenStax Prealgebra 2e (section 9.6); Archimedes' result that a sphere is two thirds of its circumscribed cylinder; unit conversions (231 cubic inches per US gallon, 0.3048 m per foot) from NIST Handbook 44, Appendix C. Related: surface area calculator, cubic yard calculator and tank volume calculator.