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Numbers · geometry · pyramidVolume of a pyramid — formula and calculator

Work out the volume of a pyramid with the formula V = ⅓ a²h — your numbers substituted and a diagram drawn. The surface area is calculated too. Units can be mixed, and the answer comes in the units you need, litres included.

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01Calculator02Formula03Example04Mistakes05Nearby06Related
01

Calculator

enter the sizes — the formula and diagram follow

Pyramid

volume · surface
a = 6 cmh = 4 cm
diagram · not to scale
Result
Volume
48cm³
= 0.000048 m³ = 0.048 L
Surface area
96cm²
= 0.0096 m²
How it was calculated
m = √((a / 2)² + h²) = √((6 / 2)² + 4²) = 5 cm
V = ⅓ a²h = 6² × 4 / 3 = 48 cm³
S = a² + 2am = 6² + 2 × 6 × 5 = 96 cm²
← Other shapes and the composite shape
02

Formula

and what each letter means
Apothem
m = √((a / 2)² + h²)
Volume
V = ⅓ a²h
Surface area
S = a² + 2am
Notation
a
side of the square base
h
height — from the apex to the centre of the base
m
apothem — the height of a side face
03

Worked example

with real numbers
Givena = 6 cm, h = 4 cm
Solution
m = √((a / 2)² + h²) = √((6 / 2)² + 4²) = 5 cm
V = ⅓ a²h = 6² × 4 / 3 = 48 cm³
S = a² + 2am = 6² + 2 × 6 × 5 = 96 cm²
Answer: volume — 48 cm³, surface area — 96 cm².
04

Common mistakes

This is a regular square pyramid. The volume is a third of a²h — don’t forget the ⅓.

The apothem and the height are different segments: the surface takes the apothem.

05

Nearby shapes

ConeV = ⅓ πr²hPrismV = S₀ × hCubeV = a³CalculatorAll 19 shapes, the composite shape and hectares →
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