Pyramid Surface Area Calculator
The surface area of a square pyramid consists of the square base and four triangular faces. The slant height l = sqrt(h² + (a/2)²) is the distance along a sloped face from the apex to the midpoint of a base edge. The lateral surface area (four triangles) is 2*a*l. The total surface area including the base is a² + 2*a*l. This calculator computes both the lateral and total surface areas from the base side length and perpendicular height.
Pyramid surface area formulas
Slant Height = √(h² + (a/2)²)
Base Area = a²
Lateral Surface Area = 2 * a * l
Total Surface Area = a² + 2 * a * l
Reference values
| Base Side | Height | Slant Height | Total Surface |
|---|---|---|---|
| 4 cm | 3 cm | 3.61 cm | 44.88 cm² |
| 6 cm | 8 cm | 8.54 cm | 138.48 cm² |
| 10 cm | 12 cm | 13.00 cm | 360.00 cm² |
Pyramid surface area calculator: frequently asked questions
What is the base area?
For a square pyramid, base area = a², where a is the side length of the square base.
What is slant height?
Slant height l = sqrt(h² + (a/2)²), the distance along a triangular face from apex to base edge midpoint.
What is lateral surface area?
Lateral (the four triangles) = 2*a*l, where a is base side and l is slant height.
What is total surface area?
Total = a² + 2*a*l = base area plus lateral surface area.
Can I solve with just slant height?
Yes. If you know slant height directly instead of h, use total = a² + 2*a*l directly.
Official sources
- Khan Academy: Volume and surface area.
- NIST: National Institute of Standards.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.