Pyramid Volume Calculator — Volume & Surface Area of a Pyramid
Find the volume and surface area of any right pyramid — square, rectangular, or equilateral-triangle base — from the base dimensions and perpendicular height.
Base shape
V = (1/3) × base area × height
- 1
Base area (side²)
6² = 36 - 2
Volume = (1/3) × base area × height
(1/3) × 36 × 8 = 96
How does this calculator work?
Pyramid volume = (1/3) × base area × height, for any base shape. Slant height l = √(h² + apothem²). Lateral surface area = ½ × base perimeter × l; total surface area = lateral area + base area. All three formulas assume a right pyramid with the apex directly above the centre of the base.
Formula
How this is calculated
The volume of any pyramid (or cone) is always one-third of the volume of the corresponding prism with the same base and height: V = (1/3) × base area × h, where h is the perpendicular height from base to apex. This result holds regardless of the base shape and follows from Cavalieri's principle.
The slant height l is the distance measured along a triangular face from the apex to the midpoint of the base edge directly below it — not the lateral edge to a corner. For a square pyramid with side b and height h, l = √(h² + (b/2)²). The lateral surface area is the sum of the areas of all triangular faces; for a right pyramid each face is an isosceles triangle with base equal to the corresponding base edge and height equal to the slant height. The total surface area adds the base area.
For a rectangular base the two pairs of opposite faces have different slant heights (because the apothems are b/2 and a/2 respectively). For an equilateral-triangle base the inradius (b / 2√3) is the apothem used in the slant height formula. Inputs share one consistent length unit; the volume is in cubic units and areas are in square units of that same measure.
Frequently asked questions
Three identical pyramids with the same square base and height can be assembled into a cube — each fills exactly one-third of the volume. This geometric fact underlies the universal V = (1/3) × base × h formula for all pyramids and cones.
The slant height is the distance from the apex to the midpoint of a base edge, measured along the face surface — used for lateral area. The lateral edge (ridge) connects the apex to a base corner and is always longer than the slant height.
The volume formula V = (1/3) × base area × h still works for oblique pyramids using the perpendicular height. However, the surface area formula using slant height is only valid for right pyramids (apex directly above the base centre); oblique pyramids need more complex treatment.
Also known as
TG we-Calculate Editorial Team. (2026). Pyramid Volume Calculator — Volume & Surface Area of a Pyramid [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/pyramid-volume-calculator
TG we-Calculate Editorial Team. "Pyramid Volume Calculator — Volume & Surface Area of a Pyramid." TG we-Calculate. 2026. https://we-calculate.com/calculator/pyramid-volume-calculator.
TG we-Calculate Editorial Team, "Pyramid Volume Calculator — Volume & Surface Area of a Pyramid," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/pyramid-volume-calculator
@misc{wecalculate_pyramid_volume_calculator, title = {Pyramid Volume Calculator — Volume & Surface Area of a Pyramid}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/pyramid-volume-calculator}}, year = {2026}, note = {TG we-Calculate} }
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