Square Pyramid Calculator — Volume, Surface Area & Slant Height
Enter the base side length and vertical height of a right square pyramid to calculate its volume, total surface area, lateral area, slant height, and lateral edge length — all from the two key measurements.
V = ⅓ × a² × h — base area times height divided by 3
V = 96
- 1
Base area
6² = 36 - 2
Base area × height
36 × 8 = 288 - 3
Volume
288 ÷ 3 = 96Any pyramid holds one-third the volume of a prism with the same base and height.
How does this calculator work?
A right square pyramid with base side a and height h has: Volume = a²h/3; slant height l = √(h² + (a/2)²); lateral surface area = 2al; total surface area = a² + 2al. Enter the two inputs to compute all dimensions instantly. The "one-third" volume rule applies to any pyramid.
Formula
How this is calculated
A right square pyramid has a square base with side length a and an apex directly above the centre at vertical height h. The volume is one-third of the base area times the height: V = (1/3) × a² × h — the same "one-third of base × height" rule that applies to any pyramid or cone.
The slant height l is the distance from the apex to the midpoint of a base edge, measured along the face. It differs from the vertical height and is found by Pythagoras on the right triangle formed by h and half the base: l = √(h² + (a/2)²). Each of the four triangular faces has area ½ × a × l, so the total lateral surface area is 4 × ½ × a × l = 2al. Adding the square base (a²) gives the total surface area a² + 2al.
The lateral edge is the straight-line distance from the apex to any base corner: e = √(h² + a²/2). This calculator assumes a perfect right pyramid where the apex is centred over the base. Oblique pyramids require different formulas.
Frequently asked questions
V = (1/3) × a² × h, where a is the base side length and h is the vertical height. For example, a pyramid with a 6-unit base and 8-unit height has volume (1/3) × 36 × 8 = 96 cubic units.
The vertical height h is the perpendicular distance from the base to the apex. The slant height l is the distance along a triangular face from the apex to the midpoint of a base edge: l = √(h² + (a/2)²). Slant height is always greater than vertical height and is used to compute the face area.
Total SA = base area + lateral area = a² + 2al, where l = √(h² + (a/2)²) is the slant height. First compute the slant height, then the lateral area (2al), and add the base (a²).
Also known as
TG we-Calculate Editorial Team. (2026). Square Pyramid Calculator — Volume, Surface Area & Slant Height [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/square-pyramid-calculator
TG we-Calculate Editorial Team. "Square Pyramid Calculator — Volume, Surface Area & Slant Height." TG we-Calculate. 2026. https://we-calculate.com/calculator/square-pyramid-calculator.
TG we-Calculate Editorial Team, "Square Pyramid Calculator — Volume, Surface Area & Slant Height," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/square-pyramid-calculator
@misc{wecalculate_square_pyramid_calculator, title = {Square Pyramid Calculator — Volume, Surface Area & Slant Height}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/square-pyramid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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