Box Surface Area Calculator
The outside area of a rectangular box — for wrapping, cardboard, plating or working out how much paint a crate takes.
A box has three pairs of matching rectangles: length × width top and bottom, length × height front and back, width × height at the two ends.
How the box surface area calculator works
A box has three pairs of matching rectangles: length × width top and bottom, length × height front and back, width × height at the two ends. Adding them gives 2(lw + lh + wh). The lateral area row leaves out the top and bottom, which is what you want for a label or a band around the sides.
Formula: cube 6a²; box 2(lw+lh+wh); sphere 4πr²; cylinder 2πr(r+h); cone πr(r+l); pyramid a² + 2a·s
Worked examples
| Inputs | Total surface area | Note |
|---|---|---|
| A 30 × 20 × 15 carton | 2,700 | 2(600 + 450 + 300) = 2,700 |
| A 2 × 3 × 4 block | 52 | 52 |
| A flat sheet-like box | 12,640 | almost all of it is the two big faces |
FAQFrequently asked questions
How do I calculate the surface area of a box?
Add the three pairs of faces: 2 × (length×width + length×height + width×height).
How much wrapping paper do I need?
The total surface area plus roughly 10–15% for overlaps and folds.
What is the lateral area for?
The four sides without the top and bottom — used for labels, banding and side panels.
Does the orientation matter?
No. Length, width and height can be entered in any order; the total is the same.
What about an open-topped box?
Subtract one length × width face from the total.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.