Volume Calculator

Calculate volume for common 3D shapes

This volume calculator covers rectangular boxes and tanks, spheres, cones, cubes, cylinders, capsules, spherical caps or domes, conical frustums, ellipsoids, square pyramids, and hollow tubes. Choose one dimension unit for every entered length, then select a cubic or liquid-capacity result unit. The calculator also reports surface area and a full equivalent-unit table.

Volume measures three-dimensional space. A length conversion is cubed when it becomes a volume conversion: one foot is 12 inches, but one cubic foot is 12³, or 1,728, cubic inches. Converting only once instead of cubing the length factor is a common source of large errors.

Rectangular box or tank volume

Multiply the inside length, width, and height. Use internal dimensions when calculating usable tank or container capacity; outside dimensions include wall thickness.

V = length x width x height

A box measuring 10 ft by 5 ft by 3 ft has a volume of 150 ft³. That is about 4,247.53 liters or 1,122.08 US gallons before allowing for wall thickness, freeboard, fittings, or unusable space.

Sphere volume

A sphere uses one radius measured from its center to the surface. Diameter is twice the radius, so divide a measured diameter by two before entering it.

V = 4/3 x pi x r³
surface area = 4 x pi x r²

A sphere with radius 3 ft has volume 36pi, or approximately 113.097 ft³.

Cylinder volume

Multiply the circular base area by the perpendicular height. The radius is half the inside diameter.

V = pi x r² x h
total surface area = 2 x pi x r x (r + h)

For a tank lying on its side and only partly filled, this full-cylinder formula is not enough because the liquid cross-section is a circular segment.

Cone volume

A right circular cone has one-third the volume of a cylinder with the same base radius and perpendicular height. Enter the vertical height, not the slanted side length.

V = 1/3 x pi x r² x h

The total surface-area estimate includes the circular base and the curved surface. The calculator derives slant height with the Pythagorean theorem.

Cube and square pyramid volume

A cube has equal edge lengths, so its volume is the edge cubed. A square pyramid has one-third the volume of a square prism with the same base edge and perpendicular height.

cube: V = a³
square pyramid: V = a² x h / 3

For a pyramid, measure height at a right angle to the base plane. A sloping edge from the apex to a base corner is not the perpendicular height.

Capsule volume

A capsule combines a cylinder with two hemispherical ends. Together, the ends form one sphere. Enter the length of only the straight cylindrical section, excluding the rounded ends.

V = pi x r² x h + 4/3 x pi x r³

The overall end-to-end length is the entered cylindrical length plus two radii.

Spherical cap and dome volume

A spherical cap is the portion cut from a sphere by a plane. It also models an idealized spherical dome. This calculator accepts three useful pairs of measurements: sphere radius and cap height, base radius and cap height, or base radius and sphere radius.

V = pi x h² x (3R - h) / 3
r² = 2Rh - h²
R = (r² + h²) / (2h)

Here, R is sphere radius, r is base radius, and h is cap height. When base radius and sphere radius are known, two caps can share the same circular base: the shallow minor cap and the deep major cap. Choose the intended side. Measurements must satisfy the sphere geometry; base radius cannot exceed sphere radius, and cap height must be greater than zero and no more than the sphere diameter.

This is an ideal geometric volume. A real dome may be a geodesic approximation, ellipsoid, paraboloid, or composite shape and may require a different model.

Conical frustum volume

A conical frustum is a cone with its tip removed by a plane parallel to the base. Enter the top radius, bottom radius, and perpendicular height.

V = pi x h x (r² + rR + R²) / 3

If the top radius is zero, the formula reduces to a cone. If both radii are equal, it reduces to a cylinder.

Ellipsoid volume

An ellipsoid uses three semi-axes measured from the center to the surface. If your measurements are full axis lengths or diameters, divide each by two before entering them.

V = 4/3 x pi x a x b x c

When all three semi-axes are equal, the ellipsoid becomes a sphere. Surface area has no simple elementary formula for a general triaxial ellipsoid, so this calculator uses the Knud Thomsen approximation for that supporting result.

Hollow tube or pipe material volume

The tube calculation subtracts the empty inner cylinder from the outer cylinder. Enter outside diameter, inside diameter, and tube length using the same unit.

V = pi x length x (outside diameter² - inside diameter²) / 4

The inside diameter must be smaller than the outside diameter. This result is the volume of tube material, not the fluid capacity. To calculate internal capacity, choose cylinder and enter the inner radius.

Volume unit conversion

How to measure for volume

• Use dimensions from the same unit system or select the correct shared input unit.
• Use inside measurements for capacity and outside measurements for displaced volume.
• Use radius, not diameter, where the form asks for radius.
• Measure cone, pyramid, and frustum height perpendicular to the base.
• Divide full ellipsoid axes by two to obtain semi-axes.
• Keep enough measurement precision until the final result; rounding each dimension early compounds the error.

Frequently asked questions

How do I calculate cubic feet?

Select feet as the dimension unit and cubic feet as the result unit. For a rectangular space, multiply length by width by height.

How do I convert cubic feet to gallons?

One cubic foot is approximately 7.480519 US gallons. Select US gallons as the output unit to convert the calculated shape volume automatically.

Is volume the same as capacity?

Volume describes three-dimensional space. Capacity usually means the usable amount a container can hold, so internal dimensions and operating allowances matter.

What is the volume of a dome?

For an ideal spherical dome, choose spherical cap and enter the sphere radius and dome height, or another supported pair. Use V = pi h²(3R - h)/3.

Can this calculate an irregular shape?

Not directly. Split a composite object into supported shapes and add or subtract their volumes, or use displacement or a specialized model for an irregular boundary.