Pyramid Surface Area Calculator
The surface area of a square pyramid — its square base plus four triangular faces, from the base side and the height.
Each of the four faces is a triangle with the base side as its base and the slant height as its height, where the slant height is √((a ÷ 2)² + h²) — measured up the middle of a face, not up an edge.
How the pyramid surface area calculator works
Each of the four faces is a triangle with the base side as its base and the slant height as its height, where the slant height is √((a ÷ 2)² + h²) — measured up the middle of a face, not up an edge. So the four faces come to 2 × a × slant, and adding the a² base gives the total. Note the slant height runs from the middle of a base edge, which is why it uses half the base side.
Formula: cube 6a²; box 2(lw+lh+wh); sphere 4πr²; cylinder 2πr(r+h); cone πr(r+l); pyramid a² + 2a·s
Worked examples
| Inputs | Total surface area | Note |
|---|---|---|
| Base 6, height 4 | 96 | slant height 5, total 96 |
| The Great Pyramid in meters | 138,391.9622 | about 138,000 m² of surface |
| A squat pyramid | 207.7033 | the base dominates |
FAQFrequently asked questions
What is the slant height of a pyramid?
The height of one triangular face, measured up the middle from the base edge to the tip: √((a÷2)² + h²).
Why half the base side?
Because the slant runs from the midpoint of a base edge, which is half a side away from the center.
Is that the same as the edge length?
No — the sloping edge from a corner to the tip is longer, √((a÷2)² × 2 + h²).
What if the pyramid is not square?
This page assumes a square base. A rectangular base has two different slant heights, one for each pair of faces.
How much of the total is the base?
The base area row shows it — for squat pyramids it is most of the surface.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.