Pick a shape and enter its measurements. You get the total surface area, the lateral (side) area, each part on its own, and the answer in other square units.
Surface area formulas
Lateral area is the sides only. Total area adds the top and bottom (the bases).
| Shape | Lateral area | Total area |
|---|
| Cube (edge s) | 4s² | 6s² |
| Rectangular box | 2h(l + w) | 2(lw + lh + wh) |
| Cylinder | 2πrh | 2πrh + 2πr² |
| Cone (slant s = √(r² + h²)) | πrs | πrs + πr² |
| Sphere | — | 4πr² |
| Hemisphere | 2πr² (dome) | 3πr² (dome + flat base) |
| Rectangular pyramid | l·√(h² + (w/2)²) + w·√(h² + (l/2)²) | lateral + lw |
| Triangular prism (sides a, b, c) | (a + b + c) × length | lateral + 2 × triangle area |
| Capsule | — | 4πr² + 2πra |
| Frustum (slant s = √((R − r)² + h²)) | π(R + r)s | π(R + r)s + πR² + πr² |
The triangle ends of a prism use Heron's formula, so you only need the three side lengths.
Worked example: a cone
A cone with radius 3 cm and height 4 cm has slant height √(3² + 4²) = 5 cm.
Lateral = π × 3 × 5 = 15π ≈ 47.124 cm²
Base = π × 3² = 9π ≈ 28.274 cm²
Total = 24π ≈ 75.398 cm²
When the result doesn't apply
- For paint, wrapping or sheet material, add extra for overlap, seams and waste. The answer is the bare outside area.
- An open-top box or a tube with no ends has less area: subtract the missing faces from the total.
- Square units don't convert like lengths: 1 square foot is 144 square inches, not 12.
Sources
How we checked this
Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:
- Box 10 × 8 × 4 ft: 304 sq ft ✓
- Cone r = 3, h = 4: lateral 15π ≈ 47.1239 ✓
- Sphere r = 5 in: 100π ≈ 314.159 in² ✓
- Square pyramid 6 × 6, height 4: slant 5, total 96 ✓
- Triangular prism 3-4-5, length 10: 132 ✓
- Prism sides 1, 2, 3 aren't a triangle ✓
Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.
Questions people ask
What is lateral surface area?
The area of the sides only, without the top and bottom. For a cylinder it's the label around a can: 2πrh.
How do I find the surface area of a box?
Add the areas of the six faces: 2 × (length × width + length × height + width × height). A 10 × 8 × 4 ft box has 2 × (80 + 40 + 32) = 304 square feet.
What is the surface area of a sphere?
4πr², exactly four times the area of a circle with the same radius. A ball with radius 5 has 100π ≈ 314.16 square units.
Why do I need the slant height for a cone or pyramid?
The sloped faces are tilted, so their true size depends on the length up the slope, not the straight-up height. The slant height comes from the Pythagorean theorem.