Surface Area Calculator
Surface area is how much material covers the outside of a solid: paint for a tank, wrapping paper for a box, sheet metal for a duct. Pick a solid and enter its dimensions.
SA = 2(lw + lh + wh)
- Volume
- 120 ft³
- V = 10 × 4 × 3 = 120 ft³
- SA = 2(40 + 30 + 12) = 164 ft²
Volume in other units
| m³ | 3.398 |
| liters | 3,398.02 |
| ft³ | 120 |
| yd³ | 4.4444 |
| in³ | 207,360 |
| US gallons | 897.662 |
| cm³ (mL) | 3,398,020 |
How to find surface area
Unfold the solid into a flat net and add up the area of every piece.
- Box: three pairs of rectangles, 2(lw + lh + wh).
- Cylinder: two circles plus a rectangle that wraps around, 2πr² + 2πrh.
- Cone: the base circle πr² plus the curved side πrs, where s is the slant height √(r² + h²).
- Sphere: 4πr² — exactly four times the area of its biggest cross-section, another result from Archimedes.
For paint, divide the surface area by the coverage on the tin (often about 350–400 ft² per US gallon per coat) and multiply by the number of coats.
Questions people ask
Lateral vs total surface area?
Lateral surface area leaves out the top and bottom faces (for a cylinder, just 2πrh). Total surface area includes them.
Why is surface area in square units?
Because it is a sum of flat areas. Only volume uses cubic units.
Does an open box include the top?
The calculator gives the closed total. For an open-top box subtract l × w once.
Stuck on a word problem?
Paste a homework question or describe your project. The AI tutor names the formula and works it through step by step. Always check the result with the calculator above.