The Volume Calculator computes the volume of cubes, spheres, cylinders, cones, and rectangular boxes (cuboids) — showing the formula applied and the numerical result.

How to Use This Calculator

1. Click the shape tab: Cube, Sphere, Cylinder, Cone, or Box.
2. Enter the required dimensions in any unit (results are in that unit³).
3. 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.

Volume Formulas Reference

• Cube: side³
• Box / rectangular prism: length × width × height
• Sphere: (4/3) × π × radius³
• Cylinder: π × radius² × height
• Cone: (1/3) × π × radius² × height

Real-World Uses

Volume calculations come up constantly: working out how much water a tank, pool, or aquarium holds; how much concrete to order for a slab; the capacity of shipping boxes; or how much soil to buy for raised garden beds. Getting the volume right prevents both costly over-ordering and the frustration of running short mid-project.

Units and Conversions

Volume uses cubic units, and small measurement errors get magnified because every dimension is multiplied together. Keep units consistent. Handy conversions: 1 cubic meter = 1,000 liters, 1 US gallon = 3.785 liters, and 1 cubic foot ≈ 7.48 US gallons. For liquids, convert your cubic result into liters or gallons to make it practical.