Volume Calculator
Calculate volume of 3D shapes: cube, sphere, cylinder, cone, pyramid, rectangular prism, and more. Volume formulas for all shapes.
1x² − 5x + 6 = 0
Discriminant = 1
two real roots
x = (−b ± √(b²−4ac)) / 2a
x₁ = 3
x₂ = 2
About the Volume Calculator
Volume measures the three-dimensional space occupied by a solid object and is essential for any task involving containers, materials, or 3D spaces. Our volume calculator computes volume for 11 common 3D shapes, with support for different unit systems. Whether you are filling a cylindrical tank, estimating concrete for a pour, or solving a geometry problem, this tool provides instant, accurate results.
Formula
Cylinder: V = πr²h | Sphere: V = (4/3)πr³ | Cone: V = (⅓)πr²h
How It Works
Key volume formulas: Cube = s³. Rectangular prism = l × w × h. Cylinder = πr²h. Sphere = (4/3)πr³. Cone = (1/3)πr²h. Pyramid = (1/3) × base area × h. Torus = 2π²Rr² where R is the major radius and r is the minor radius. All formulas assume regular, uniform shapes — irregular volumes require integration or physical measurement (water displacement).
Tips & Best Practices
- ✓1 cubic foot = 7.48 US gallons. 1 cubic metre = 1,000 litres.
- ✓A standard bath holds 60-80 gallons; an Olympic swimming pool holds 660,000 gallons.
- ✓Concrete is ordered in cubic yards: 1 cubic yard = 27 cubic feet.
- ✓Aquarium volume: multiply length × width × height in inches, then divide by 231 for US gallons.
- ✓Gravel, sand, and soil are sold by the cubic yard in the USA and cubic metre in Europe.
Who Uses This Calculator
Contractors ordering concrete and fill material, aquarium hobbyists calculating tank volumes for stocking and chemistry, chemical engineers designing storage tanks, students completing geometry assignments, and homeowners estimating pool volumes for chemical treatment all use volume calculations.
Optimised for: USA · Canada · UK · Australia · Calculations run in your browser · No data stored
Frequently Asked Questions
How do you calculate the volume of a cylinder?
Volume = π × r² × h. For a cylinder with radius 4 and height 10: V = π × 16 × 10 ≈ 502.7 cubic units.