Surface Area Calculator
Calculate surface area of cubes, rectangular prisms, spheres, cylinders, cones, and pyramids.
Returns total and lateral area in square inches, cm, and meters.
Surface area is the total area of all outer faces of a three-dimensional shape. It is measured in square units (cm², m², in², ft²) and is essential for calculating material needs — paint, wrapping, insulation, packaging.
Common surface area formulas:
Cube (side length s): SA = 6s² Example: cube with 4 cm sides → SA = 6 × 16 = 96 cm²
Rectangular box / cuboid (length l, width w, height h): SA = 2(lw + lh + wh) Example: box 10 × 5 × 3 cm → SA = 2(50 + 30 + 15) = 190 cm²
Sphere (radius r): SA = 4πr² Example: sphere r = 6 cm → SA = 4 × π × 36 = 452.4 cm²
Cylinder (radius r, height h): SA = 2πr² + 2πrh (top + bottom + side) Example: r = 3 cm, h = 10 cm → SA = 56.5 + 188.5 = 245 cm²
Cone (radius r, slant height l): SA = πr² + πrl (base + lateral face) Example: r = 4 cm, l = 7 cm → SA = 50.3 + 87.9 = 138.2 cm²
Worked example — how much paint for a room? Room: 4 m × 5 m × 2.5 m high, two coats on walls only. Wall area = 2(4 × 2.5) + 2(5 × 2.5) = 20 + 25 = 45 m² Two coats = 90 m² At 10 m² per litre of paint → need 9 litres
Why surface area matters:
- Packaging design (minimise material for a given volume)
- Heat exchange (larger SA = faster cooling or heating)
- Drug delivery (tablet surface area affects how fast it dissolves)
- Architecture and construction material estimation