Home › Math & Science › Volume Calculator

Volume Calculator

Our free volume calculator works out how much space a shape holds, in cubic inches, cubic feet, cubic centimeters, or cubic meters. Pick a shape — a rectangular box, a cylinder, a sphere, a cone, a cube, a square pyramid, a triangular prism, an ellipsoid, a capsule, a torus, a cone frustum, a triangular pyramid, a hollow cylinder, or a hemisphere — enter your measurements, and the volume appears right away, with the formula and each step shown. A labelled diagram beside the calculator shows the shape and every measurement, so you can see exactly what to measure.

How it works

Volume is the amount of three-dimensional space an object takes up. If area tells you how much paint covers a wall, volume tells you how much water fills a tank, how much concrete fills a footing, or how many moving boxes fit in a storage unit. In the United States it is usually measured in cubic inches, cubic feet, or cubic yards, and in metric work in cubic centimeters or cubic meters.

Each shape has its own formula, but the idea is the same: multiply the measurements that define the shape, using pi (about 3.14159) for anything round. A rectangular box is the simplest case — length times width times height. A cylinder is the area of its circular base, pi times the radius squared, times its height. A sphere uses four-thirds pi times the radius cubed, and a cone is exactly one-third of the cylinder with the same base and height, which is why its formula is one-third pi r squared h. A cube is just a box with all sides equal, so its volume is the side length cubed. A square pyramid holds one-third of the volume of a box with the same base and height. A triangular prism is the area of its triangular face — one-half base times height — times the prism length. An ellipsoid stretches a sphere along three axes, so its volume is four-thirds pi times a times b times c. A capsule is a cylinder with a hemisphere on each end, and the two hemispheres together make a full sphere, so its volume is pi r squared times the cylinder length plus four-thirds pi r cubed. A torus is a ring, and its volume is two pi squared times the major radius times the minor radius squared. A cone frustum is a cone with its top cut off, so its volume uses both radii and the height: one-third pi h times R squared plus R times r plus r squared. A triangular pyramid holds one-third of the volume of a triangular prism with the same base and height. A hollow cylinder is a tube, so subtract the inner cylinder from the outer one: pi h times R squared minus r squared. A hemisphere is exactly half a sphere, so its volume is two-thirds pi r cubed.

The most common mistake is mixing units or using the diameter where the radius belongs. If a pipe is 6 inches across, its radius is 3 inches — using 6 would make the answer four times too big, because the radius is squared. Likewise, if the length is in feet and the height is in inches, convert one to match the other first. This calculator keeps it simple: pick one unit for every measurement, and the answer comes out in the matching cubic unit, such as ft³ for feet or cm³ for centimeters.

Volume is a practical number in everyday American life. Movers quote storage units in cubic feet, so a 10-by-10-foot unit with an 8-foot ceiling holds about 800 cubic feet. Concrete and mulch are sold by the cubic yard — 27 cubic feet — so a patio slab 10 feet by 12 feet and 4 inches thick needs about 1.5 cubic yards of concrete. Aquariums are rated in gallons, and one cubic foot of water is about 7.48 gallons, which is how a tank's size turns into a weight your floor has to carry.

Worked example

A family in Texas is packing for a move and wants to know how much a standard moving box holds. The box measures 2 feet long, 3 feet wide, and 4 feet tall. Select "Rectangular box" and "Feet" in the calculator, then enter 2, 3, and 4.

The formula for a box is V = l × w × h. Step 1 — multiply length by width: 2 × 3 = 6 square feet, the area of the base. Step 2 — multiply by the height: 6 × 4 = 24. The box holds 24 cubic feet. That is the same answer the calculator shows for 2 × 3 × 4 ft: 24 ft³. For a sense of scale, that is roughly the size of a large moving box that can hold about a dozen folded moving blankets, or around 180 gallons of water if it were a tank — far more than most people guess from the outside dimensions.

FAQ