Pyramid Calculator
Enter the square base edge and height of a pyramid to find its volume, slant height and surface area.
units
units
- 1
Square the base edge (b²)
6 × 6 = 36 - 2
Slant height = √((b⁄2)² + h²)
√((6 ÷ 2)² + 8²) = 8.544Distance from the apex down the center of a triangular face to a base edge. - 3
Volume = ⅓ × b² × h
⅓ × 36 × 8 = 96
Formula
How this is calculated
This tool models a right square pyramid: a square base of edge b with the apex directly above the base center at a vertical height h. Both inputs use the same generic length unit, so volume comes out in those units cubed and areas in units squared. Both values must be positive; zero or negative entries produce no result.
The volume is one third of the box that shares the base and height, giving 1⁄3 × b² × h, the same one-third rule that applies to cones and other pyramids. The slant height is the slope distance from the apex down the centerline of a triangular face to the midpoint of a base edge. It is found with the Pythagorean theorem from the vertical height and half the base edge: √((b⁄2)² + h²), and is always longer than h.
The total surface area sums the square base, b², and the four identical triangular faces, each ½ × b × slant, which combine to 2 × b × slant. The model assumes a perfectly symmetric pyramid with the apex centered, so a tilted (oblique) apex would change the face slants and is not covered here.
Examples
| Input | Result |
|---|---|
| base = 6, height = 8 | Volume = 96, Slant ≈ 8.5440, Surface ≈ 138.5280 |
About this calculator
A square pyramid has a square base and four triangular faces meeting at a single apex above the base center. Like a cone, its volume is one third of the prism with the same base and height, giving 1⁄3 × b² × h.
The slant height is the distance from the apex down the middle of a triangular face to the base edge, found from the half-base and the vertical height by the Pythagorean theorem. The total surface area adds the square base (b²) to the four triangular faces (2 × b × slant).
Frequently asked questions
Use Volume = 1⁄3 × base² × height. A base edge of 6 and height of 8 gives a volume of 96 cubic units.
It is the distance from the apex to the midpoint of a base edge, equal to √((b⁄2)² + h²). It differs from the vertical height, which goes straight down to the base center.
Yes. The total surface area here is the square base (b²) plus the four triangular sides (2 × b × slant height).
Also known as
TG we-Calculate Editorial Team. (2026). Pyramid Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/pyramid-calculator
TG we-Calculate Editorial Team. "Pyramid Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/pyramid-calculator.
TG we-Calculate Editorial Team, "Pyramid Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/pyramid-calculator
@misc{wecalculate_pyramid_calculator, title = {Pyramid Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/pyramid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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