The Volume Of A Pyramid Calculator
A pyramid holds exactly one third of the prism built on the same base with the same height, whatever the shape of that base.
Volume
72
- Base area
- 24
- Area of the four faces
- 93.2646
- Total surface area
- 117.2646
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
volume = base area x height / 3
- V
- Volume inside the pyramid
- B
- Area of the base
- h
- Perpendicular height from base to apex
How to check the result by hand
- 1
Work out the area of the base
Length times width for a rectangle, side squared for a square, half base times height for a triangle. The volume formula accepts any of these.
- 2
Measure the perpendicular height
Straight up from the base to the apex, not along a sloping edge. If you only have a slant height, recover the perpendicular height with Pythagoras.
- 3
Multiply base area by height
Twenty four times nine is two hundred and sixteen. This is the volume of the prism, which is three times too large.
- 4
Divide by three
Two hundred and sixteen divided by three is seventy two cubic units. The division is what turns the prism into the pyramid that fits inside it.
- 5
Convert to litres if the answer is a capacity
Base dimensions in decimetres give litres directly, or convert cubic metres by multiplying by a thousand. The one third applies before any unit conversion, not after.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Volume Of A Pyramid page.