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Box Surface Area & Diagonal

There are three pairs of matching faces, so add the three products and double. The space diagonal is the square root of all three squares added — Pythagoras in three dimensions.

Your numbers

Surface area

5,900cm²

Volume

30,000cm³

Diagonal

55.9cm

Litres

30L

Formula

Surface area = 2 × (Length × Width + Width × Depth + Depth × Length)

Courier size limits usually go by the sum of the three edges. Two boxes of equal volume can differ on whether they qualify.

What to enter

InputDefaultAccepted range
Length (cm)The measurement across, side to side.400 and up
Width (cm)The measurement front to back.300 and up
Depth (cm)How deep it goes.250 and up

Step by step

FormulaSurface area = 2 × (Length × Width + Width × Depth + Depth × Length)
With the default numbersSurface area = 2 × (40 × 30 + 30 × 25 + 25 × 40)
AnswerSurface area = 5,900 cm²

Quick reference table

Results when only Length (cm) changes and everything else stays put.

Length (cm)Surface area (cm²)Volume (cm³)Diagonal (cm)
203,70015,00043.87
304,80022,50049.24
405,90030,00055.9
608,10045,00071.59
8010,30060,00089.02

What each result means

ResultAt default values
Surface area (cm²)The total area of a solid’s outer skin.5,900
Volume (cm³)The space a solid holds — length cubed.30,000
Diagonal (cm)Corner to opposite corner.55.9
Litres (L)Capacity in litres; one litre is 1,000 cm³.30

Common mistakes

Courier size limits usually go by the sum of the three edges. Two boxes of equal volume can differ on whether they qualify.

Glossary

Length
The measurement across, side to side.
Width
The measurement front to back.
Depth
How deep it goes.
Surface area
The total area of a solid’s outer skin.
Volume
The space a solid holds — length cubed.
Diagonal
Corner to opposite corner.
Litres
Capacity in litres; one litre is 1,000 cm³.

Frequently asked questions

Q. How is Box Surface Area & Diagonal calculated?

Surface area = 2 × (Length × Width + Width × Depth + Depth × Length) — There are three pairs of matching faces, so add the three products and double. The space diagonal is the square root of all three squares added — Pythagoras in three dimensions.

Q. Can you walk through an example?

With Length 40cm, Width 30cm, Depth 25cm, the answer is Surface area 5,900cm².

Q. What do I need to enter?

Enter Length, Width, Depth. The result recalculates as you type, and an empty box counts as zero.

Q. How much does the answer move if I change a number?

Changing only Length (cm) moves the answer to Length (cm) 20 → Surface area (cm²) 3,700 and Length (cm) 80 → Surface area (cm²) 10,300. The table below lays out five steps.

Q. How are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

Q. Anything to watch out for?

Courier size limits usually go by the sum of the three edges. Two boxes of equal volume can differ on whether they qualify.

Related calculators

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.