Volume Calculator — Cube, Cylinder, Sphere & More

Free online volume calculator for 7 shapes: cube, rectangular prism, cylinder, sphere, cone, square pyramid, and triangular prism. Pick a shape to get the formula and result instantly, plus surface area for cylinders, spheres, and cones.

Last updated: 2026-09-06

Volume formulas by shape

Shape	Formula
Cube	Volume = side × side × side
Rectangular prism	Volume = length × width × height
Cylinder	Volume = π × radius² × height, Surface area = 2π×radius² + 2π×radius×height
Sphere	Volume = (4/3) × π × radius³, Surface area = 4π×radius²
Cone	Volume = (1/3) × π × radius² × height, Surface area = π×radius² + π×radius×slant height
Square pyramid	Volume = (1/3) × side² × height
Triangular prism	Volume = base area (triangle) × prism length

The volume's unit is the cube of whatever length unit you entered (e.g. enter values in cm and the result is in cm³). Surface area is in the square of that unit.

What volume calculation is

Calculating volume means working out how much space a solid — a cube, a cylinder, a sphere — occupies, from measurements such as the length of an edge or a radius. The formula differs with the kind of solid: a cylinder is “area of the base × height”, a sphere is “(4/3) × π × radius³”, and so on, so you have to pick the formula that belongs to the solid in front of you.

This tool lets you choose among seven solids — cube, rectangular prism, cylinder, sphere, cone, square pyramid and triangular prism — and calculates the volume automatically once you enter the measurements it asks for. For the cylinder, the sphere and the cone it also gives the surface area at the same time, so you get a correct result straight away even if the formula has slipped your mind.

How to calculate volume

Choose the solid Select the one you want from cube, rectangular prism, cylinder, sphere, cone, square pyramid and triangular prism.
Enter the measurements Fields appear for the edge length, the length, width and height, the radius and so on, according to the solid you chose. Enter them in a single consistent unit — all in centimetres, for instance.
Read the volume and surface area The volume is worked out as you type. For the cylinder, sphere and cone the surface area is shown alongside it.

Tips for getting more out of it

While the Area Calculator handles 2D shapes, this tool is its 3D counterpart. Prisms and pyramids both use the shared idea of "base area × height" (or × 1/3), so understanding the area formulas makes the volume formulas click faster.
When estimating how much lumber or concrete you need for a DIY project, calculating the volume of a rectangular prism or cylinder first helps you avoid ordering too much or too little material.
To find the capacity of a fish tank or water tank, pick a cylinder or rectangular prism, enter the interior dimensions in centimeters, and divide the resulting volume (cm³) by 1,000 to convert to liters.
The slant height a cone needs for its surface area (the distance from the apex to a point on the base circle) is computed automatically from the radius and height, so there's no need to work out the Pythagorean theorem by hand.
A pyramid or cone's volume is always exactly one third of a prism or cylinder with the same base and height. Keeping that 1/3 ratio in mind alongside the formulas makes them much easier to remember for homework.

Where volume calculation helps

Working out the capacity of an aquarium or water tank

Enter the internal measurements of a cylinder or a rectangular prism in centimetres and you get the volume in cubic centimetres; divide by 1,000 to convert it to litres.

Estimating materials for DIY

When a project uses timber or concrete, calculating the volume of the rectangular prism or cylinder beforehand tells you in advance whether you will have too much or too little.

Homework and exam preparation

Seven formulas from the cube to the cone are set out together, which serves both for checking your own working while learning them and for revising the geometry topic.

Estimating volumes for 3D printing or packaging

Choose the solid closest to your model or carton, enter the measurements, and you get a rough estimate of the material needed or the capacity of the packaging.

Terms used in volume calculation

Base area: The area of the face that forms the base of a cylinder, prism, cone or pyramid. In most cases the volume comes from “base area × height”, or a third of that.
Slant height: The length of the straight line from the apex of a cone to a point on the circumference of its base. It follows from the radius and the height by Pythagoras’ theorem — calculated here for you — and is needed for the cone’s surface area.
Surface area: The total area of every outer face of a solid. Where volume is expressed in cubed units (cm³ and the like), surface area is expressed in squared units (cm² and the like).
Prisms and pyramids: A prism is a solid whose two bases are congruent polygons and whose sides are parallelograms; a pyramid has a polygonal base and triangular sides meeting at a point. The rectangular prism and the square pyramid are the familiar examples.
Method of exhaustion: The approach used by the mathematicians of ancient Greece, which divides a figure into ever finer parts to derive relationships between areas and volumes. It served to prove that a pyramid has a third of the volume of a prism on the same base and of the same height.

FAQ

A cube is a special rectangular prism where all edges are equal in length. A rectangular prism can have a different length, width, and height, while a cube only needs one side length entered to compute its volume.

The slant height is the straight-line distance from the cone's apex to a point on the edge of its base. Given the base radius and height, it can be computed automatically using the Pythagorean theorem (slant² = radius² + height²) — this tool uses exactly that formula internally to get the surface area.

Ancient Greek mathematicians such as Eudoxus and Democritus demonstrated this relationship using an early technique called the method of exhaustion. Intuitively, a triangular prism can be split into three congruent tetrahedra (pyramids), and you can also confirm it experimentally: filling a prism-shaped container by pouring in water from a pyramid-shaped mold of the same base and height takes exactly three pourings.

This tool doesn't assume a specific length unit, so the volume's unit is simply the cube of whatever unit you entered. For example, if you enter lengths in centimeters, read the volume as cm³ (cubic centimeters). Surface area comes out in the square of that unit (e.g. cm²).

This relationship comes from building up a sphere's volume as a stack of infinitely thin spherical shells. In fact, differentiating the sphere's volume formula with respect to the radius r gives exactly the surface area formula, 4πr² — because the extra volume gained from a tiny increase in radius is approximately the sphere's surface area at that moment times the thickness of the increase.

Side Note — the cylinder-and-sphere relationship Archimedes had carved on his tombstone

The ancient Greek mathematician Archimedes discovered that a sphere and the cylinder that exactly circumscribes it (a cylinder with the same height and diameter as the sphere) always have a volume ratio of 2:3. The cylinder's volume is πr²×2r = 2πr³, and the sphere's volume is (4/3)πr³, giving exactly 2πr³ : (4/3)πr³ = 3 : 2. Archimedes was said to be so proud of this discovery that he requested a diagram of a cylinder and an inscribed sphere be carved on his tombstone.

The fact that a pyramid or cone's volume equals one third of a prism or cylinder with the same base and height is credited to the mathematician Eudoxus, working around the 4th century BCE, and was later recorded in Euclid's "Elements". That geometers arrived at this kind of near-limit reasoning (the method of exhaustion) more than two millennia before calculus was formalized is one of the notable milestones in the history of geometry.

Calculating the volume of everyday solids still matters a great deal today, from sizing water tanks and estimating 3D-printer material usage to computing box capacity for packaging design. The formulas themselves have barely changed since antiquity, but the range of their applications keeps expanding.

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