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.

Volume Calculator (Multi-Solid)

Calculate the volume of common 3D geometric solids. Choose a shape, enter the dimensions, and get the volume instantly with the formula shown. Supported shapes include spheres, cylinders, cones, cubes, rectangular boxes, triangular prisms, and rectangular pyramids.

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Standard geometric formulae All volumes use exact standard formulae with pi = 3.141592653589793.

1. Choose a Shape

Shape

Units

2. Enter Dimensions

Radius (r)

Height (h)

Base radius (r)

Height (h)

Side length (a)

Length (l)

Width (w)

Height (h)

Triangle base (b)

Triangle height (h_t)

Prism length (l)

Base length (l)

Base width (w)

Height (h)

Formula used V = π × r² × h

Volume Result

Volume
-
cubic metres (m³)

Shape

Cylinder

Selected solid

Scientific Notation

For large / small values

Worked Example (matches default inputs) A cylinder with radius 3 m and height 10 m:
V = π × 3² × 10 = π × 9 × 10 = 282.743 m³

Calculation Detail

ShapeCylinder

Inputs usedr = 3 m, h = 10 m

FormulaV = πr²h

Volume282.743 m³

Unit Conversions

Cubic metres-

Cubic centimetres-

Litres-

Cubic feet-

Cubic inches-

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

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.

Understanding Volume Units

1 cubic metre (m3) = 1,000 litres = 1,000,000 cm3. For everyday use, litres are convenient for liquids and small volumes; cubic metres for building materials. The conversion panel below your result shows all common units automatically.

Related Calculators

Maths and Stats Calculators: full hub for geometry and statistics tools.
Surface Area Calculator (multi-solid): find the surface area of the same set of solids.
Cube Surface Area and Volume Calculator: dedicated tool for cubes with additional detail.
Pyramid Volume and Surface Area Calculator: dedicated pyramid tool with slant height.
Rectangular Box (Cuboid) Calculator: volume, surface area, and diagonal for boxes.
Area Calculator (multi-shape): calculate the area of 2D shapes.

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.

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