Volume Calculator
Find the volume of spheres, cones, cubes, cylinders, rectangular prisms, square pyramids and capsules.
Inputs
Volume
113.097336
Solid
sphere
Step by step
Formula
V = (4/3)πr³
Substitute
V = (4/3) × π × 3³ = (4/3) × π × 27
Volume
= 113.09733553
How it works
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
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.