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
| Input | Default | Accepted range |
|---|---|---|
| Length (cm)The measurement across, side to side. | 40 | 0 and up |
| Width (cm)The measurement front to back. | 30 | 0 and up |
| Depth (cm)How deep it goes. | 25 | 0 and up |
Step by step
Quick reference table
Results when only Length (cm) changes and everything else stays put.
| Length (cm) | Surface area (cm²) | Volume (cm³) | Diagonal (cm) |
|---|---|---|---|
| 20 | 3,700 | 15,000 | 43.87 |
| 30 | 4,800 | 22,500 | 49.24 |
| 40 | 5,900 | 30,000 | 55.9 |
| 60 | 8,100 | 45,000 | 71.59 |
| 80 | 10,300 | 60,000 | 89.02 |
What each result means
| Result | At 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.