Surface Area of a Square Pyramid Calculator
Enter the base side length and vertical height of a square pyramid to find its total surface area, slant height, lateral area and volume — all from TSA = b² + 2bs.
units
units
Square base + four congruent triangular faces: b² + 2b·s
- 1
Slant height
√(5² + (6 ÷ 2)²) = √(25 + 9) = 5.831Distance from the apex straight down the face to the midpoint of a base edge. - 2
Base area
6² = 36 - 3
Lateral area (4 triangular faces)
2 × 6 × 5.831 = 69.9714 - 4
Total surface area
36 + 69.9714 = 105.9714
How does this calculator work?
A square pyramid with base side b and height h has slant height s = √(h²+(b/2)²) and total surface area TSA = b² + 2bs (base plus four congruent triangular faces). Lateral area alone = 2bs. Volume = ⅓b²h. Enter base side and height in the same unit.
Formula
How this is calculated
A square pyramid has a square base of side length b and four congruent isosceles triangular faces that meet at an apex directly above the centre of the base. The slant height s is the distance from the midpoint of a base edge to the apex, and it follows from the Pythagorean theorem: s = √(h² + (b/2)²), where h is the vertical height and b/2 is the distance from the base centre to the midpoint of an edge.
Each of the four triangular faces has base b and height s, so its area is ½bs. The four faces together give the lateral area 4 × ½bs = 2bs. Adding the square base area b² gives the total surface area: TSA = b² + 2bs.
The volume (V = ⅓b²h) is included for completeness. All inputs must be positive and share the same unit. This formula applies to a right square pyramid — one where the apex is directly over the centre of the base. Oblique pyramids require a different approach.
Frequently asked questions
Vertical height (h) is the perpendicular distance from the apex straight down to the base. Slant height (s) is the distance from the apex down the middle of a triangular face to the midpoint of a base edge. Slant height is always longer than vertical height: s = √(h² + (b/2)²).
A square pyramid is a special case of a rectangular pyramid where the base length equals the base width (l = w = b). Because all base edges are equal, all four triangular faces are congruent and share one slant height, simplifying the formula to TSA = b² + 2bs.
Classic examples include calculating the material needed for pyramid-shaped packaging, tent covers or architectural facades. The Egyptian pyramids' surface area can be estimated with this formula using their known base and height dimensions.
Also known as
TG we-Calculate Editorial Team. (2026). Surface Area of a Square Pyramid Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/surface-area-of-square-pyramid-calculator
TG we-Calculate Editorial Team. "Surface Area of a Square Pyramid Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/surface-area-of-square-pyramid-calculator.
TG we-Calculate Editorial Team, "Surface Area of a Square Pyramid Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/surface-area-of-square-pyramid-calculator
@misc{wecalculate_surface_area_of_square_pyramid_calculator, title = {Surface Area of a Square Pyramid Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/surface-area-of-square-pyramid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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