How this calculator works
Choose a solid shape and enter its dimensions to get its volume using the matching geometric formula. Box, cylinder, sphere, and cone are the four solids people most often need volume for, whether that is packing boxes, filling a tank, or sizing a scoop.
Volume is always expressed in cubic units: if a length is entered in centimeters, the result is in cubic centimeters (cm³); in feet, cubic feet (ft³). All three (or two, for a sphere or cone) dimensions must be entered in the same unit for the result to be meaningful.
How do you calculate volume?
Box: Volume = length × width × heightCylinder: Volume = π × radius² × heightSphere: Volume = (4/3) × π × radius³Cone: Volume = (1/3) × π × radius² × heightA cone is always exactly one-third the volume of a cylinder with the same radius and height, and a sphere is exactly two-thirds the volume of the cylinder that tightly encloses it (Archimedes' hat-box theorem).
Worked example: a cone with radius 3 and height 6
- Square the radius: 3² = 9.
- Multiply by height: 9 × 6 = 54.
- Multiply by π and one-third: 54 × π ÷ 3 = 18π ≈ 56.5487 cubic units.
Frequently asked questions
Why is a cone's volume one-third of a cylinder's?
This is a classical result from integral calculus (or Cavalieri's principle): a cone tapers linearly from the full circular base to a point, and integrating its cross-sectional area over the height gives exactly one-third of the cylinder with the same base and height.
What is Archimedes' hat-box theorem?
It states that a sphere's volume equals two-thirds of the volume of the smallest cylinder that contains it (radius equal to the sphere's radius, height equal to the sphere's diameter). Archimedes considered this one of his most important discoveries.
How precise is π in this calculator?
It uses JavaScript's Math.PI constant, accurate to about 15-16 significant decimal digits, far more precise than the 3.14 or 22/7 approximations commonly used by hand.
Can I find the volume of a cube with this calculator?
Yes — a cube is just a box where length, width, and height are all equal. Enter the same value in all three fields in the box mode.
How do I find the volume of a half-sphere (hemisphere)?
Take half of the full sphere formula: hemisphere volume = (2/3) × π × radius³, exactly half of (4/3) × π × radius³. For a sphere of radius 1, the full sphere's volume is (4/3) × π ≈ 4.18879 cubic units, so a hemisphere of the same radius has a volume of (2/3) × π ≈ 2.0944 cubic units.