Volume Calculator (Multi-Solid)

This calculator works out the volume of seven common three-dimensional solids: sphere, cylinder, cone, cube, rectangular box (cuboid), triangular prism, and rectangular pyramid. Volume tells you how much space a shape encloses, and getting it right matters whether you are ordering concrete for a post hole, sizing a water tank, working out shipping space, or checking a geometry homework answer. Start by choosing your shape from the dropdown and selecting a unit of measurement (centimetres, metres, millimetres, inches, or feet), then enter the dimensions the shape needs, such as radius and height for a cylinder, or length, width, and height for a box. The result updates instantly and shows the volume in your chosen cubic unit, the exact formula used, the shape selected, and the value in scientific notation for large or small results. A calculation detail panel confirms the inputs used, and a unit conversion table automatically shows the same volume in cubic metres, cubic centimetres, litres, cubic feet, and cubic inches, so you do not need to convert by hand. Make sure every dimension you enter is in the same unit before calculating; mixing centimetres and metres will give a wrong answer. The maths is exact for the numbers you provide, but if you are ordering materials like concrete, soil, or gravel, add a margin for wastage and compaction on top of the calculated figure.

Volume Result

Volume
282.743 m3
cubic metres (m) (m3)

Shape

Cylinder

Selected solid

Scientific Notation

2.8274e+2 m3

For large / small values

Volume Formulae for Common Solids

Volume measures the amount of three-dimensional space enclosed by a shape. It is expressed in cubic units (cm3, m3, litres, etc.). The table below lists the standard formula for each solid supported by this calculator.

Solid	Formula	Variables
Sphere	V = (4/3) x pi x r3	r = radius
Cylinder	V = pi x r2 x h	r = base radius, h = height
Cone	V = (1/3) x pi x r2 x h	r = base radius, h = height
Cube	V = a3	a = side length
Rectangular box (cuboid)	V = l x w x h	l = length, w = width, h = height
Triangular prism	V = (1/2) x b x h_t x l	b = triangle base, h_t = triangle height, l = prism length
Rectangular pyramid	V = (1/3) x l x w x h	l = base length, w = base width, h = height

Solid

Formula

Variables

Sphere

V = (4/3) x pi x r3

r = radius

Cylinder

V = pi x r2 x h

r = base radius, h = height

Cone

V = (1/3) x pi x r2 x h

r = base radius, h = height

Cube

V = a3

a = side length

Rectangular box (cuboid)

V = l x w x h

l = length, w = width, h = height

Triangular prism

V = (1/2) x b x h_t x l

b = triangle base, h_t = triangle height, l = prism length

Rectangular pyramid

V = (1/3) x l x w x h

l = base length, w = base width, h = height

How to Use This Calculator

Select the 3D solid from the Shape dropdown, choose the unit of measurement for your dimensions, then enter the required values. The volume updates instantly and the formula used is shown below the inputs. The unit conversion panel at the bottom converts your result into cubic metres, cubic centimetres, litres, cubic feet, and cubic inches automatically.

All dimensions must be in the same unit. If your radius is in centimetres and your height is in metres, convert one before entering values.

Practical Uses

Concrete and fill: Calculate how many cubic metres of concrete, soil, or gravel you need to fill a cylindrical post hole, rectangular trench, or conical pile.

Water storage: Estimate the capacity of a cylindrical tank or rectangular reservoir in litres.

Packaging: Work out how much space a product occupies for shipping calculations.

Science and engineering: Volume is used in density, pressure, flow rate, and thermodynamics calculations.

Maths study: Check your homework answers for geometry problems involving 3D shapes.

Related Calculators

Sources and method: Standard Euclidean geometry formulae as taught in NCEA Level 1 to 3 Mathematics and widely referenced in engineering handbooks (e.g. Machinery's Handbook). Pi is taken as 3.141592653589793 (double-precision floating point).

Results are mathematically exact for the inputs provided, subject to floating-point precision. Ensure all dimensions are in the same unit before calculating.

Frequently asked questions

What is the formula for the volume of a sphere?

The volume of a sphere is V = (4/3) x pi x r^3, where r is the radius. For a sphere with a radius of 5 cm, V = (4/3) x 3.14159 x 125 = 523.60 cm3. The formula grows quickly because volume scales with the cube of the radius: doubling the radius increases the volume by a factor of 8.

How do I find the volume of a cylinder?

The volume of a cylinder is V = pi x r^2 x h, where r is the radius of the circular base and h is the height (or length) of the cylinder. For example, a cylinder with a radius of 3 cm and a height of 10 cm has a volume of 3.14159 x 9 x 10 = 282.74 cm3. If you know the diameter rather than the radius, halve it first.

Why is the volume of a cone one-third of a cylinder?

The formula for a cone is V = (1/3) x pi x r^2 x h, which is exactly one-third of the volume of a cylinder with the same base and height. This relationship is a geometric fact that can be proven by calculus (integration) or by physical demonstration: it takes exactly three cone-fills of water to fill a cylinder of the same base radius and height. The same one-third relationship holds between a rectangular pyramid and a rectangular prism.

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Volume Calculator (Multi-Solid)

1. Choose a Shape

2. Enter Dimensions