Volume Calculator
Find the volume of spheres, cones, cubes, cylinders, pyramids and more.
About Volume Calculator
Volume measures the three-dimensional space enclosed by a solid. Sphere: (4/3)πr³. Cone: (1/3)πr²h. Cube: a³. Cylinder: πr²h. Rectangular prism: l × w × h. Square pyramid: (1/3)a²h where a is the base side. Capsule (cylinder capped by two hemispheres): πr²h + (4/3)πr³.
Formulas
Sphere
V = (4/3)πr³
Cone
V = (1/3)πr²h
Cube
V = a³
Cylinder
V = πr²h
Rectangular prism
V = l × w × h
Square pyramid
V = (1/3)a²h
Capsule
V = πr²h + (4/3)πr³
Worked example
With the default values below, Volume Calculator returns Volume of 113.097336. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Solidone of Sphere, Cone, Cube, Cylinder, Rectangular Prism (Box), Square Pyramid, Capsule
- Sphere
- Radius (r)minimum 0
- 3
- Height (h)minimum 0
- 6
- Side length (a)minimum 0
- 4
- Length (l)minimum 0
- 5
- Width (w)minimum 0
- 4
- Base side length (a)minimum 0
- 4
Results
- Volume
- 113.097336
- Solid
- sphere
Step by step
- 1Formula
- 2Substitute
- 3Volume= 113.09733553
Assumptions and limits
- The result is derived only from the 7 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the volume of a sphere with radius 3?
V = (4/3)π × 3³ = (4/3) × π × 27 = 36π ≈ 113.097. This is a classic example because 36π has an exact closed form.
Why does a cone have 1/3 of the cylinder's volume?
Cavalieri's principle and calculus show that stacking infinitely thin circular slices that taper linearly from base to apex gives exactly (1/3)πr²h. Three identical cones exactly fill one cylinder of the same dimensions.
What units should I use?
Any consistent length unit works. If you enter centimetres, the volume is in cm³. To convert: 1 m³ = 1 000 000 cm³; 1 litre = 1000 cm³; 1 gallon ≈ 3785 cm³.