Right Rectangular Pyramid Calculator — Volume & Surface Area
Enter the base length, base width and perpendicular height of a right rectangular pyramid to find its volume, slant heights, lateral faces, total surface area and lateral edge.
units
units
units
V = ⅓ × l × w × h
- 1
Base area = l × w
8 × 6 = 48 - 2
Volume = ⅓ × base area × h
⅓ × 48 × 10 = 160Any pyramid's volume is one third of the prism with the same base and height.
How does this calculator work?
For a right rectangular pyramid with base l×w and height h: Volume = ⅓lwh, slant heights sₗ = √(h²+(w/2)²) and sᵥᵥ = √(h²+(l/2)²), Lateral SA = l·sₗ + w·sᵥᵥ, Total SA = lw + l·sₗ + w·sᵥᵥ. Enter all three dimensions — results are in the corresponding squared and cubed units.
Formula
How this is calculated
A right rectangular pyramid has a rectangular base of length l and width w, and an apex located directly above the centre of that base at perpendicular height h. There are four triangular lateral faces: two with base l and two with base w.
Volume is one third of the base area times height: V = ⅓ × l × w × h, just like any pyramid. The two slant heights measure from the apex down to the midpoints of the two types of base edge. The slant height to the midpoint of an l-edge (crossing the width) is sₗ = √(h² + (w/2)²), and the slant height to the midpoint of a w-edge is sᵥᵥ = √(h² + (l/2)²), both by Pythagoras. Each triangular face area is ½ × base × slant height for that face, so lateral SA = 2 × (½lsₗ) + 2 × (½wsᵥᵥ) = l·sₗ + w·sᵥᵥ. Adding the rectangular base area lw gives the total surface area.
The lateral edge connects the apex to a corner of the base. Because the apex is above the centre of the base, the horizontal distance from the centre to a corner is √((l/2)² + (w/2)²), so the lateral edge is √(h² + (l/2)² + (w/2)²). All formulas assume the apex is exactly above the centre; inputs must be positive.
Frequently asked questions
A rectangular base has two different edge lengths l and w. The apex is above the centre, so the perpendicular distance from it to the midpoint of an l-edge differs from the distance to the midpoint of a w-edge. Each gives a different slant height for the corresponding pair of triangular faces.
Slant height runs from the apex to the midpoint of a base edge (it is the height of a triangular face). The lateral edge runs from the apex to a corner of the base — it is longer than either slant height and equals √(h² + (l/2)² + (w/2)²).
A right square pyramid is the special case where l = w (square base). It has one unique slant height and four identical triangular faces. Enter equal length and width here to compute that special case.
Also known as
TG we-Calculate Editorial Team. (2026). Right Rectangular Pyramid Calculator — Volume & Surface Area [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/right-rectangular-pyramid-calculator
TG we-Calculate Editorial Team. "Right Rectangular Pyramid Calculator — Volume & Surface Area." TG we-Calculate. 2026. https://we-calculate.com/calculator/right-rectangular-pyramid-calculator.
TG we-Calculate Editorial Team, "Right Rectangular Pyramid Calculator — Volume & Surface Area," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/right-rectangular-pyramid-calculator
@misc{wecalculate_right_rectangular_pyramid_calculator, title = {Right Rectangular Pyramid Calculator — Volume & Surface Area}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/right-rectangular-pyramid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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