Volume Calculator

Volume calculator at a glance#

A volume calculator finds the space inside a 3D shape from its dimensions. The formula depends on the shape: a cube is side cubed, a box is length times width times height, a cylinder is pi times radius squared times height, and a sphere is four-thirds pi times radius cubed.

Worked example for a box: a container 4 cm long, 3 cm wide, and 2 cm tall holds 4 × 3 × 2 = 24 cubic centimeters. For round shapes, pi is about 3.14159, so a cylinder with radius 3 cm and height 10 cm holds pi × 3² × 10, which is about 282.7 cm³.

Keep every dimension in the same unit before you multiply, since the answer comes out in that unit cubed. Enter your shape and measurements in the calculator above for the exact volume, and convert to liters or gallons with the same tool. Rounding pi changes the last digits slightly.

Volume formulas for common shapes#

Volume is the space inside a 3D shape, measured in cubic units such as cm³, m³, or ft³. The formula depends on the shape. The table above covers the cube, box, cylinder, and sphere; the cone and capsule are below.

Cone#

A cone tapers from a circular base to a single point. Its volume is one-third of the matching cylinder: V = ⅓πr²h, where r is the base radius and h is the height. For a cone with radius 3 cm and height 4 cm, V = ⅓ × π × 3² × 4 = about 37.7 cm³.

Capsule#

A capsule is a cylinder with a hemisphere on each end, the shape of many pills. Add the cylinder body to a full sphere of the same radius: V = πr²h + &frac43;πr³, where h is the length of the straight middle section. For radius 2 cm and a 5 cm middle, V = (π × 2² × 5) + (&frac43; × π × 2³) = about 96.3 cm³.

Worked checks for round shapes#

A sphere with radius 12 cm holds &frac43; × π × 12³ = about 7,238 cm³. A cylinder with radius 7 cm and height 10 cm holds π × 7² × 10 = about 1,539 cm³. Use π ≈ 3.14159; rounding it changes only the last digits.

Irregular shapes#

For a shape that is not a standard solid, split it into parts you can measure (a box plus a half-cylinder, for example), find each volume, and add them. True freeform shapes need calculus, but breaking them into simple solids is accurate enough for most practical work.

Convert between volume units#

The tool doubles as a converter between cubic meters, cubic feet, cubic inches, liters, and gallons. Keep every dimension in the same unit before you multiply, since the result comes out in that unit cubed. One liter equals 1,000 cm³.

FAQ#

How do I calculate the volume of a cube?#

Cube the side length: V = s³. A cube with 3 m sides holds 3³ = 27 m³.

How is the volume of a cylinder calculated?#

Multiply the base area by the height: V = πr²h. With radius 4 cm and height 10 cm, V = π × 4² × 10 = about 502.65 cm³.

How do I find the volume of a sphere?#

Use V = &frac43;πr³. A sphere with a 7 cm radius holds &frac43; × π × 7³ = about 1,436.76 cm³.

Can it handle irregular shapes?#

Split the object into standard solids, calculate each, and add them. Accuracy depends on how closely those solids match the real shape.

What units does it support?#

Cubic meters, cubic feet, cubic inches, liters, and gallons, with conversions between them. One liter equals 1,000 cm³.