The Volume Calculator computes the volume of cubes, spheres, cylinders, cones, and rectangular boxes (cuboids) — showing the formula applied and the numerical result.
Volume Calculator
Calculate the volume of common 3D shapes.
How to Use This Calculator
- Click the shape tab: Cube, Sphere, Cylinder, Cone, or Box.
- Enter the required dimensions in any unit (results are in that unit³).
- Click Calculate Volume.
Volume Formulas Quick Reference
- Cube: V = a³ (where a is the side length)
- Sphere: V = (4/3) × π × r³
- Cylinder: V = π × r² × h
- Cone: V = (1/3) × π × r² × h
- Box (cuboid): V = l × w × h
Why Volume Calculations Matter
Shipping: Carriers use dimensional weight (volume × factor) when it exceeds actual weight. Knowing your box volume helps estimate shipping costs.
Aquariums: A 24″×12″×16″ aquarium holds approximately 19.9 gallons. Calculate gallons from cubic inches by dividing by 231.
Cooking: Scaling recipes up or down for different bowl or pot sizes requires knowing volumes. A cylindrical pot with twice the radius has four times the volume (r² relationship).
Construction: Concrete is sold by the cubic yard. A 10×10 ft patio 4 inches thick = 1.23 cubic yards.
Frequently Asked Questions
How do I convert cubic inches to gallons?
Divide by 231. For liters, divide cubic centimeters by 1,000.
Why is the cone formula 1/3 of the cylinder?
A cone occupies exactly 1/3 of the volume of a cylinder with the same base radius and height — a result from calculus (integration of circular cross-sections from tip to base). You can verify this physically by filling a cone with water and pouring it into the matching cylinder three times to fill it.
How it works
Each shape uses its standard 3D geometry formula. π is JavaScript's Math.PI. Results are computed to full floating-point precision and rounded to 8 significant figures for display.Formula
Cube: V=a³. Sphere: V=(4/3)πr³. Cylinder: V=πr²h. Cone: V=(1/3)πr²h. Box: V=l×w×h