Rectangular Pyramid Volume Calculator — Volume & Surface Area
Enter the base length, base width and perpendicular height of a rectangular pyramid to find its volume, surface areas, slant heights and apex-to-corner edge instantly.
units
units
units
V = ⅓ × l × w × h
- 1
Base area
l × w = 8 × 6 = 48 - 2
Enclosing prism volume
base area × h = 48 × 5 = 240 - 3
Pyramid volume
(1 ÷ 3) × 240 = 80A pyramid is exactly one-third the volume of the enclosing rectangular prism.
How does this calculator work?
Volume of a rectangular pyramid = (1/3) × l × w × h. Lateral surface area = l × √(h² + (w/2)²) + w × √(h² + (l/2)²). Total surface area adds the base l × w. Enter base dimensions and height in the same unit; volume is in that unit cubed.
Formula
How this is calculated
A rectangular pyramid has a rectangular base of length l and width w, and a single apex directly above the centroid of the base at perpendicular height h. Its volume is exactly one-third the volume of the enclosing rectangular prism: V = (1/3) × l × w × h. This one-third factor applies to all pyramids regardless of base shape — a result provable by Cavalieri's principle or integration.
The lateral surface consists of four triangular faces in two pairs. The pair of faces whose base spans the length l has slant height s₁ = √(h² + (w/2)²), where w/2 is the horizontal distance from the midpoint of those edges to the foot of the apex. The pair spanning width w has slant height s₂ = √(h² + (l/2)²). Total lateral area = l × s₁ + w × s₂, and total surface area adds the rectangular base l × w.
The apex-to-corner (lateral) edge connects the apex to any base corner and has length √(h² + (l/2)² + (w/2)²) — the 3-D Pythagorean distance. All formulas assume a right pyramid where the apex is directly above the base centroid; oblique pyramids require a different approach. Slant height and lateral edge are equal only when l = w (square base).
Frequently asked questions
Three congruent pyramids with the same rectangular base and height can be assembled into one rectangular prism, so each pyramid has volume = ⅓ × base area × height. This can be proved rigorously with Cavalieri's principle or by integrating thin horizontal cross-sections whose area shrinks linearly from the base to the apex.
Perpendicular height h is the straight vertical distance from the apex down to the base. Slant height is the distance from the apex to the midpoint of a base edge, measured along the surface of a triangular face. For a rectangular base: s₁ = √(h² + (w/2)²) and s₂ = √(h² + (l/2)²) for the two pairs of opposite faces.
Yes — set l = w to get a square-base pyramid. Both slant heights will be equal and all four triangular faces will be congruent isosceles triangles. The Great Pyramid of Giza (base ≈ 230 m × 230 m, original height ≈ 146 m) can be estimated using this calculator.
Also known as
TG we-Calculate Editorial Team. (2026). Rectangular Pyramid Volume Calculator — Volume & Surface Area [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rectangular-pyramid-volume-calculator
TG we-Calculate Editorial Team. "Rectangular Pyramid Volume Calculator — Volume & Surface Area." TG we-Calculate. 2026. https://we-calculate.com/calculator/rectangular-pyramid-volume-calculator.
TG we-Calculate Editorial Team, "Rectangular Pyramid Volume Calculator — Volume & Surface Area," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rectangular-pyramid-volume-calculator
@misc{wecalculate_rectangular_pyramid_volume_calculator, title = {Rectangular Pyramid Volume Calculator — Volume & Surface Area}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rectangular-pyramid-volume-calculator}}, year = {2026}, note = {TG we-Calculate} }
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