Volume Calculator

Volume is the amount of three-dimensional space an object occupies or a container can hold. It is measured in cubic units, such as cubic feet or cubic centimeters, because it combines three lengths. Doubling every dimension of a shape multiplies its volume by eight, which is why a slightly larger pot or tank holds noticeably more than it looks.

Every formula on this page comes from one of two ideas. Prisms and cylinders have the same cross-section all the way through, so their volume is simply the base area times the height. Shapes that taper to a point, like cones and pyramids, hold exactly one third of the matching prism. Spheres, caps and ellipsoids follow from calculus but end up with equally compact formulas. You can enter each dimension in a different unit; the calculator converts everything before multiplying.

Sphere

A sphere is the set of points that are all the same distance, the radius, from a center point. Balls, bubbles and planets are close approximations. Its volume is four thirds of π times the radius cubed. Because the radius is cubed, a ball with twice the radius holds eight times as much.

Archimedes discovered that a sphere fills exactly two thirds of the smallest cylinder that encloses it, a result he was so proud of that he asked for it to be carved on his tomb. A basketball with a radius of 4.7 inches has a volume of about 435 cubic inches.

• V = 4/3 × π × r³

Cone

A right circular cone has a circular base and sides that taper evenly to a single point, the apex, directly above the center of the base. Its volume is one third of the volume of a cylinder with the same base and height. The same one-third rule holds for any cone or pyramid, whatever the shape of its base, and even when the apex is off center, as long as the height is measured straight up from the base.

A traffic cone with a base radius of 0.15 m and a height of 0.7 m encloses about 0.0165 m³, or 16.5 liters. A paper snow-cone cup with a 4 cm radius and 10 cm height holds about 168 cm³.

• V = 1/3 × π × r² × h

Cube

A cube is a box whose six faces are identical squares, so all twelve edges have the same length. Its volume is the edge length cubed, which is where the word cubed comes from. A cube with 3-foot edges holds 27 cubic feet. The cube is also the reference shape behind every cubic unit: one cubic meter is the space inside a cube one meter on each side, and one liter is a cube 10 centimeters on each side.

• V = a³

Cylinder

A cylinder has two parallel, identical circular ends joined by a curved side. Cans, pipes and many storage tanks are cylinders. Its volume is the area of the circular base, πr², multiplied by the height. This calculator's cylinder form is labelled with the tank names it uses because a cylindrical tank is the most common practical case.

To find how many gallons a round tank holds, compute the volume in cubic feet and multiply by about 7.48. A tank 4 feet across and 6 feet tall has a radius of 2 feet, a volume of π × 4 × 6 ≈ 75.4 ft³, and a capacity of roughly 564 gallons. The formula also works for an oblique cylinder whose sides lean, provided the height is measured perpendicular to the base.

• V = π × r² × h

Rectangular Tank

A rectangular tank, or rectangular prism, is a box whose faces are all rectangles. Rooms, shipping containers, aquariums and moving boxes are everyday examples. Its volume is length times width times height. An aquarium 36 inches long, 18 inches wide and 20 inches tall holds 12,960 cubic inches, which is about 56 US gallons since one gallon is 231 cubic inches.

• V = l × w × h

Capsule

A capsule is a cylinder capped at each end by a hemisphere of the same radius, the shape of a pill, a propane tank or a pressure vessel. Its volume is the cylinder part plus the two hemispheres, which together make one full sphere. In the formula, h is the length of the straight cylindrical section only. Rounded ends spread pressure evenly, which is why the shape is common for tanks that hold compressed gas.

• V = π × r² × h + 4/3 × π × r³

Spherical Cap

A spherical cap is the piece cut off a sphere by a flat plane, like the top of a dome or the liquid in the bottom of a round flask. It is described by three related measurements: the radius R of the sphere it came from, the radius r of its flat circular base, and its height h from the base to the top. Knowing any two determines the third, since r² = h(2R − h).

The volume is π h² (3R − h) ÷ 3. When h equals R the cap is a hemisphere and the formula gives two thirds of π R³, half a sphere, as expected. When h equals 2R it becomes the whole sphere. If you only know the base radius and the height, the sphere's radius is R = (r² + h²) ÷ (2h), and the volume can also be written as π h (3r² + h²) ÷ 6.

A practical use is finding how much liquid is in a partly filled spherical tank: the liquid forms a cap whose height is the depth of the liquid.

• V = 1/3 × π × h² × (3R − h)
• r² = h × (2R − h)

Conical Frustum

A frustum is what remains when the top of a cone is sliced off parallel to its base. Buckets, lampshades, flower pots and drinking cups are usually frustums. It has a bottom radius R, a smaller top radius r and a height h.

The volume can be found by subtracting the small missing cone from the full cone, which simplifies to π h (r² + rR + R²) ÷ 3. When r is zero the frustum becomes an ordinary cone, and when r equals R it becomes a cylinder, so the formula agrees with both. A bucket with a 15 cm top radius, 12 cm bottom radius and 30 cm height holds about 17.2 liters.

• V = 1/3 × π × h × (r² + r × R + R²)

Ellipsoid

An ellipsoid is a sphere that has been stretched or squashed along its three axes. It is described by three semi-axes a, b and c, the distances from the center to the surface along each axis. Eggs, rugby balls and the Earth itself, which bulges slightly at the equator, are approximately ellipsoids.

The volume is four thirds of π times the product of the three semi-axes. When all three are equal the ellipsoid is a sphere and the formula reduces to the sphere formula. The Earth's equatorial radius is about 6,378 km and its polar radius about 6,357 km, giving a volume of roughly 1.083 × 10¹² cubic kilometers.

• V = 4/3 × π × a × b × c

Square Pyramid

A square pyramid has a square base and four triangular faces that meet at an apex above the center of the base. Its volume is one third of the base area times the height, the same one-third relationship as a cone. Three identical square pyramids can be fitted together to fill a cube when each has a height equal to its base edge, which is a neat way to see where the one third comes from.

The Great Pyramid of Giza originally had a base edge of about 230.3 m and a height of about 146.6 m, which gives a volume of roughly 2.6 million cubic meters.

• V = 1/3 × a² × h

Tube Pyramid

A tube, or hollow cylinder, is a cylinder with a smaller cylinder removed from its center. Pipes, hoses, straws and rings are tubes. Its volume is the volume of the outer cylinder minus the volume of the hole. Written with diameters, which are easier to measure on a pipe, it is π (d₁² − d₂²) ÷ 4 times the length, where d₁ is the outer diameter and d₂ the inner diameter.

This gives the volume of material in the wall, which is what you need to estimate the weight of a pipe. For the volume a pipe can carry, use the cylinder formula with the inner radius instead. A steel pipe with a 60 mm outer diameter, a 50 mm inner diameter and a length of 2 m contains about 1.73 liters of steel, which at roughly 7.85 kg per liter weighs around 13.6 kg.

• V = π × (d₁² − d₂²) ÷ 4 × l

Common Volume Units

The table converts common volume units to cubic meters and liters. US customary and imperial gallons differ, so check which one a figure uses.

Frequently asked questions