Surface Area Calculator
Calculate the total surface area, lateral surface area, base area, and volume of a cube, prism, sphere, cylinder, cone, pyramid, or ellipsoid.
Surface Area Formula Reference
| Shape | Total Surface Area | Lateral Surface Area | Volume |
|---|---|---|---|
| Cube (a) | 6a² | 4a² | a³ |
| Rectangular Prism (l,w,h) | 2(lw+lh+wh) | 2h(l+w) | lwh |
| Sphere (r) | 4πr² | 4πr² | (4/3)πr³ |
| Cylinder (r,h) | 2πr(r+h) | 2πrh | πr²h |
| Cone (r,l) | πr(r+l) | πrl | (1/3)πr²h |
| Pyramid – Sq. Base (a,l) | a²+2al | 2al | (1/3)a²h |
| Triangular Prism (a,b,c,h) | bh+(a+b+c)·L | (a+b+c)·L | (1/2)b·h·L |
| Ellipsoid (a,b,c) | ≈4π·((a^p·b^p+a^p·c^p+b^p·c^p)/3)^(1/p), p≈1.6075 | N/A | (4/3)πabc |
Calculate the total surface area, lateral surface area, base area, and volume of eight common 3D solids, from cubes and cylinders to triangular prisms and ellipsoids.
How Surface Area Calculator Works
Total surface area (TSA) adds up the area of every face of the solid, while lateral surface area (LSA) excludes the top and bottom base(s) — for example, a cylinder's LSA = 2πrh covers just the curved side, while its TSA = LSA + 2×(base area) adds in the two circular ends.
Shapes with a slanted face — cones and pyramids — first compute their slant height using the Pythagorean theorem (a cone's slant length is √(r²+h²)) before applying it to the lateral area formula, since the slant length, not the vertical height, is the actual surface distance from the base edge up to the apex.
The triangular prism uses Heron's formula to find its triangular base area from three side lengths, then multiplies the base triangle's perimeter by the prism's length to get lateral area. The ellipsoid uses the same Knud Thomsen approximation (exponent p≈1.6075) as the Volume Calculator, since there is no exact closed-form formula for an ellipsoid's surface area.
See It In Action
Who Uses Surface Area Calculator and Why
- Estimating how much material wraps around a cylindrical container's curved side only, using lateral surface area.
- Calculating the full material needed for a fully enclosed storage tank or box using total surface area.
- Finding a cone or pyramid's slant-based surface area for a tent, roof, or awning design.
- Computing a triangular prism's surface area from just its three base side lengths.
Mistakes to Avoid
- Confusing lateral surface area with total surface area when estimating material for a fully enclosed object — lateral area specifically excludes the top and bottom bases.
- Using the vertical height instead of the slant height for a cone or pyramid's lateral surface — the slant height is always longer and is the actual surface distance from the base edge to the apex.
- Expecting an exact figure for the ellipsoid's surface area rather than the Knud Thomsen approximation, which is accurate to only within about 1%.
Tips for Best Results
- Decide upfront whether your project needs total surface area (a fully enclosed object) or just lateral surface area (an open-ended shape, like a label wrapping a can).
- Let the calculator derive the slant height automatically from the vertical height and base dimensions using the Pythagorean theorem, rather than estimating it yourself.
Fixing Common Problems
My lateral and total surface area values came out identical. — Double-check you actually meant to compare the two — for shapes where the base area contributes very little relative to the sides, the two values can be close but should still differ; if they're exactly equal, confirm your shape and dimension inputs.
Terms Explained
Lateral surface area (LSA): The area of a solid's 'side' faces only, excluding the top and/or bottom base(s).
Slant height: The distance along a cone or pyramid's slanted face from the base edge to the apex, found via the Pythagorean theorem and always longer than the vertical height.