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Surface area of a box (cuboid)

The total area of the six rectangular faces of a box.

S = 2(lw + lh + wh)

Cube of side s

S = 6s²

Calculator

The live calculator needs JavaScript. The worked example below shows the same steps it would.

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Volume = lwh = 30
Surface area = 2(lw + lh + wh) = 62
Space diagonal = √(l² + w² + h²) = 6.1644

What the symbols mean

$S$: the total surface area
$l$: the length
$w$: the width
$h$: the height

When to use it

Use it for how much card, paint, wrapping paper or sheet metal a box needs. For an open box (no lid) subtract one $l w$ face.

Worked example

How much card is needed to make a closed box 5 cm long, 3 cm wide and 2 cm high? (l = 5, w = 3, h = 2)

Start from the formula.
$S = 2 (l w + l h + w h)$
Substitute $l$ = $5$ , $w$ = $3$ , $h$ = $2$ and work it out.
$S = 2 \cdot (5 \cdot 3 + 5 \cdot 2 + 3 \cdot 2)$
$= 2 \cdot (15 + 10 + 6)$
$= 2 \cdot (25 + 6)$
$= 2 \cdot 31$
$= 62$

Answer S = 62 cm²

Why it works

A box has three pairs of identical opposite faces: top and bottom ( $l w$ each), front and back ( $l h$ ), and the two ends ( $w h$ ).

Common mistakes

Counting each face once instead of twice.
Including a lid that is not there (or leaving out one that is).
Confusing surface area (cm²) with volume (cm³).