Surface Area Calculator
Surface area of a cube, box, sphere, cylinder, cone or square pyramid — total and curved — with the volume alongside for painting, wrapping, plating and heat-loss work.
Surface area adds up every face.
How the surface area calculator works
Surface area adds up every face. A box has three pairs of rectangles; a cylinder is two circles plus a rectangle rolled round; a cone is a circle plus a sector whose radius is the slant height √(r² + h²); a square pyramid is a square plus four triangles of slant height √((a/2)² + h²). A sphere is the one that is not obvious: its area is exactly four times the area of the circle you would see looking at it.
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 |
|---|---|---|
| Cube with 3 cm sides | 54 | 54 cm² — six faces of 9 |
| Box 2 × 3 × 4 | 52 | 52 |
| Sphere of radius 2 | 50.2655 | 4π(2²) ≈ 50.265 |
| Cylinder r 2, h 5 | 87.9646 | 2π×2×7 ≈ 87.965 |
| Cone r 3, h 4 | 75.3982 | slant 5, area 24π ≈ 75.398 |
FAQFrequently asked questions
What is the difference between total and curved area?
Curved (or lateral) area leaves out the flat ends — the label on a tin, not its lid and base. Total adds them.
Why is a sphere 4πr²?
Archimedes proved it equals the curved area of the cylinder that just contains it. It is exactly four times the circle you see looking at the sphere.
What is slant height?
The distance up the sloping face of a cone or pyramid, √(r² + h²) for a cone — longer than the vertical height.
What units does it use?
Whatever you enter: enter centimeters and the area is square centimeters and the volume cubic centimeters.
Why does surface area to volume matter?
It governs how fast something heats, cools or dries. Small things have far more surface for their size, which is why crushed ice melts faster than a block.
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)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.