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Numbers · geometry · rectangular boxVolume of a box — formula and calculator

Work out the volume of a box with the formula V = a × b × c — 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

Rectangular box

volume · surface
a = 5 cmc = 2.7 cmb = 4 cm
diagram · not to scale
Result
Volume
54cm³
= 0.000054 m³ = 0.054 L
Surface area
88.6cm²
= 0.00886 m²
How it was calculated
V = a × b × c = 5 × 4 × 2.7 = 54 cm³
S = 2(ab + bc + ac) = 2 × (5 × 4 + 4 × 2.7 + 5 × 2.7) = 88.6 cm²
← Other shapes and the composite shape
02

Formula

and what each letter means
Volume
V = a × b × c
Surface area
S = 2(ab + bc + ac)
Notation
a
length
b
width
c
height
03

Worked example

with real numbers
Givena = 5 cm, b = 4 cm, c = 2.7 cm
Solution
V = a × b × c = 5 × 4 × 2.7 = 54 cm³
S = 2(ab + bc + ac) = 2 × (5 × 4 + 4 × 2.7 + 5 × 2.7) = 88.6 cm²
Answer: volume — 54 cm³, surface area — 88.6 cm².
04

Common mistakes

Cubic metres do not convert like metres: 1 m³ = 1,000,000 cm³ and 1000 litres.

For the volume of a room the height is floor to ceiling, not to the top of the door.

05

Nearby shapes

CubeV = a³PrismV = S₀ × hRectangleS = a × bCalculatorAll 19 shapes, the composite shape and hectares →
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