Pyramid Volume Calculator
The volume of a rectangular pyramid — a third of the box that would contain it.
A pyramid holds one third of the prism with the same base and height, so the volume is ⅓ × base area × height.
How the pyramid volume calculator works
A pyramid holds one third of the prism with the same base and height, so the volume is ⅓ × base area × height. For a rectangular base that is ⅓ × length × width × height. The rule does not care about the base shape, so the same third applies to square, rectangular and triangular pyramids alike.
Formula: cone ⅓πr²h; pyramid ⅓lwh; torus 2π²Rr²; hemisphere ⅔πr³; ellipsoid ⁴⁄₃πabc
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| Base 6 × 6, height 9 | 108 | 108 |
| The Great Pyramid, 230 m square and 146 m high | 2,574,466.6667 | about 2.58 million m³ |
| A rectangular pyramid 10 × 4 by 6 | 80 | 80 |
FAQFrequently asked questions
What is the volume of a pyramid?
A third of the base area times the height: ⅓ × l × w × h for a rectangular base.
Does the base shape matter?
Only for working out the base area. The one-third rule is the same for square, rectangular and triangular bases.
Which height do I use?
The perpendicular height from the base to the apex, not the sloping edge or face.
How big is the Great Pyramid?
About 2.58 million cubic metres, from a 230 m square base and 146 m original height.
What if the apex is off-centre?
The volume is the same. Only the perpendicular height matters.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.