Surface Area Calculator
Surface, lateral and base area and volume of a cube, box, sphere, hemisphere, cylinder, cone, frustum, pyramid, prism or capsule, with slant and diagonal.
Total and lateral surface area, one base area, volume, the slant height where it exists, the space diagonal of a box or cube, the area-to-volume ratio and the formula used.
Example: A 3 × 4 × 12 box has 192 surface (168 lateral), volume 144 and a 13 space diagonal; a cone of radius 3 and height 4 has slant 5, lateral 15π and total 24π.
Lateral is the side;
total adds the bases.
The formulas for each solid, what lateral and base mean, and the assumptions for the pyramid and prism.
The solids
Cube 6a² and a³; box 2(lw + wh + lh) and lwh with the space diagonal √(l² + w² + h²); sphere 4πr² and 4/3 πr³; hemisphere 3πr² (curved 2πr² plus the flat face) and 2/3 πr³; cylinder 2πr² + 2πrh and πr²h; cone with slant l = √(r² + h²): πr² + πrl and 1/3 πr²h; conical frustum with slant √((R − r)² + h²): π(R + r)l plus both circles, volume πh(R² + Rr + r²)/3; capsule 4πr² + 2πrL and πr²L + 4/3 πr³.
Pyramids and prisms
A right square pyramid of base a and height h has slant √((a/2)² + h²), lateral area 2al and volume a²h/3; a rectangular pyramid has two slants, one for each pair of faces, and the lateral area is the sum. The triangular prism takes the triangle as isosceles for its perimeter (base b, height h_t, equal sides √((b/2)² + h_t²)); base area and volume hold for any triangle with that base and height.
Reading the numbers
Lateral area is the curved or side surface without the bases; "base" is one base; total is everything. Area ÷ volume is given as the surface-to-volume ratio. Units are yours — squared and cubed. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Closed-form solid geometry: box 2(lw + wh + lh), sphere 4πr², cylinder 2πr² + 2πrh, cone πr² + πr·√(r² + h²), frustum π(R + r)·l + πR² + πr², pyramid base + ½·perimeter·slant
Last reviewed 21 September 2026. How results are checked: How we verify.