# Free online volume calculator

> Volume is the amount of 3-D space a shape occupies. This calculator finds volume and surface area for six common shapes in your choice of unit.

Calculate volume and surface area for cubes, rectangular boxes, spheres, cylinders, cones, and rectangular pyramids. Works in cm, m, inches, or feet.

**Interactive version:** https://onlinecalculator.me/math/volume/
**Category:** Math

## How to use

1. Choose a **shape** from the dropdown.
2. Choose a **unit** (cm, m, in, ft).
3. Enter the required dimensions — the form shows only the fields relevant to your shape.
4. Volume and surface area appear instantly.

## Formulas

### Cube (side = s)
- Volume: V = s³
- Surface area: A = 6s²

### Rectangular box (l × w × h)
- Volume: V = l × w × h
- Surface area: A = 2(lw + lh + wh)

### Sphere (radius = r)
- Volume: V = (4/3)πr³
- Surface area: A = 4πr²

### Cylinder (radius = r, height = h)
- Volume: V = πr²h
- Surface area: A = 2πr(r + h)

### Cone (radius = r, height = h)
- Slant height: l = √(r² + h²)
- Volume: V = (1/3)πr²h
- Surface area: A = πr(r + l)

### Rectangular pyramid (base l × w, height = h)
- Volume: V = (1/3) × l × w × h
- Slant heights: s₁ = √((l/2)² + h²), s₂ = √((w/2)² + h²)
- Surface area: A = lw + l × s₂ + w × s₁

## Worked examples

**Sphere, r = 5 cm:** V = (4/3)π(5³) ≈ **523.5988 cm³**, A = 4π(25) ≈ **314.1593 cm²**

**Cylinder, r = 4, h = 10 cm:** V = π(16)(10) ≈ **502.6548 cm³**, A = 2π(4)(14) ≈ **351.8584 cm²**

## Notes

- All results are rounded to four decimal places.
- Surface area for a cone includes the base circle and the lateral face.
- For a pyramid, surface area includes the rectangular base and all four triangular faces.

## Frequently asked questions

### Which shapes does this calculator support?

Cube, rectangular box, sphere, cylinder, cone, and rectangular pyramid. Select the shape from the dropdown and the relevant input fields appear automatically.

### How is the volume of a sphere calculated?

V = (4/3) × π × r³, where r is the radius. Surface area = 4 × π × r².

### How is the volume of a cylinder calculated?

V = π × r² × h, where r is the radius and h is the height. Surface area = 2 × π × r × (r + h).

### How is the volume of a cone calculated?

V = (1/3) × π × r² × h. Surface area = π × r × (r + slant height), where slant height = √(r² + h²).

### How is the volume of a rectangular pyramid calculated?

V = (1/3) × base length × base width × height. Surface area includes the base plus four triangular faces.

### What units can I use?

Centimeters (cm), meters (m), inches (in), or feet (ft). Volume is shown in cubic units (e.g. cm³) and surface area in square units (e.g. cm²).

## Sources

- [Volume](https://en.wikipedia.org/wiki/Volume) — Wikipedia
- [Volume](https://mathworld.wolfram.com/Volume.html) — Wolfram MathWorld

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