Volume Calculator
Calculate the volume of common 3D shapes.
Cube
Sphere
Cylinder
Cone
Quick Examples
Volume Formulas
| Shape | Formula | Units |
|---|---|---|
| Cube | V = s^3 | cubic units |
| Sphere | V = (4/3) pi r^3 | cubic units |
| Cylinder | V = pi r^2 h | cubic units |
| Cone | V = (1/3) pi r^2 h | cubic units |
| Rectangular Prism | V = l w h | cubic units |
| Pyramid | V = (1/3) B h | B = base area |
What is Volume?
Volume is the amount of three-dimensional space occupied by an object. It's measured in cubic units like cubic meters (m3), liters (L), or gallons.
How to Use This Volume Calculator
- Choose the shape: click Cube, Sphere, Cylinder, or Cone at the top of the tool.
- Enter the dimensions the shape asks for — side length for a cube, radius for a sphere, or radius and height for a cylinder or cone.
- Use one unit everywhere: mixing centimeters and meters silently corrupts the answer.
- Click "Calculate Volume": the result appears instantly with the formula used.
What Is Volume?
Volume is the amount of three-dimensional space an object occupies or can hold. While area measures a flat surface in square units, volume measures a solid in cubic units — the unit of your measurements, cubed. Centimeters become cubic centimeters (cm³), feet become cubic feet (ft³).
Volume Formulas Explained
- Cube: V = s³. A cube is the side length multiplied by itself three times — the simplest volume there is.
- Rectangular prism (box): V = length × width × height. The most common real-world volume.
- Sphere: V = (4/3) × π × r³. The 4/3 factor comes from calculus, but the formula is easy to use.
- Cylinder: V = π × r² × h. Think of it as the circular base area (πr²) stacked h units tall.
- Cone: V = (1/3) × π × r² × h — exactly one-third the volume of a cylinder with the same base and height. Three cones of sand fill one matching cylinder.
- Pyramid: V = (1/3) × B × h, where B is the base area. Same one-third rule as the cone.
Worked Examples
Moving box
A box 4 ft long, 3 ft wide, and 2 ft tall holds V = 4 × 3 × 2 = 24 ft³.
Cylinder (can or pipe)
A cylinder with radius 3 cm and height 10 cm: V = π × 9 × 10 ≈ 282.74 cm³.
Sphere (ball)
A sphere with radius 5 cm: V = (4/3) × π × 125 ≈ 523.60 cm³.
Cone
A cone with radius 4 cm and height 9 cm: V = (1/3) × π × 16 × 9 ≈ 150.80 cm³ — exactly one-third of the cylinder it would fit inside.
Cube
A cube with side 5 cm: V = 5³ = 125 cm³.
Volume vs Capacity: Unit Conversions
Capacity (liters, gallons) is just volume expressed in liquid-friendly units:
| Conversion | Value |
|---|---|
| 1 m³ | 1,000 liters |
| 1 liter | 1,000 cm³ (1 cm³ = 1 mL) |
| 1 ft³ | 28.3168 liters |
| 1 ft³ | 7.4805 US gallons |
| 1 US gallon | 3.7854 liters |
Aquarium example: a tank 100 cm × 40 cm × 50 cm holds V = 100 × 40 × 50 = 200,000 cm³ = 200 liters.
Where Volume Calculations Matter
- Shipping and moving: box volumes determine how many fit in a truck or storage unit.
- Aquariums and pools: volume tells you how much water — and how much treatment chemical — you need.
- Cooking and chemistry: scaling a recipe or a solution up means scaling volumes, not just lengths.
- Construction: concrete, soil, and mulch are ordered by cubic volume.
Common Mistakes
- Entering the diameter as the radius: sphere, cylinder, and cone formulas all need r — halve the diameter first.
- Forgetting the one-third: cones and pyramids are one-third of their matching cylinder/prism, not equal to it.
- Mixing units: a radius in inches with a height in feet produces garbage. Convert first.
- Reporting volume in square units: volume is cubic (cm³), never cm².
Tip: for containers you fill — tanks, planters, dumpsters — measure the inside dimensions. Wall thickness eats into usable volume, sometimes by more than you expect.
Pyramids and Prisms
Square pyramid: V = (1/3) × base area × height. A pyramid on a 6 × 6 base, 9 tall: V = (1/3) × 36 × 9 = 108 cubic units.
Triangular prism: V = (triangle area) × length. A prism with a triangular face of base 6 and height 4, extruded 10 long: V = (½ × 6 × 4) × 10 = 120 cubic units.
How Volume Scales
Doubling one dimension doubles the volume; doubling all dimensions multiplies it by 8. A cube of side 2 holds 8; a cube of side 4 holds 64. Doubling only a cylinder's radius quadruples its volume (the r² effect) — a small widening buys a lot of capacity.
The Displacement Method
For irregular objects, Archimedes' trick still works: submerge the object in water and measure the rise. If the water level goes from 300 mL to 475 mL, the object displaces 175 mL — so its volume is 175 cm³.