Pyramid Volume Calculator
Find the volume, slant height, edge length and surface areas of a square-based pyramid.
Last updated · View algorithm, constants and default inputs (JSON)
Volume (unit³)
About this calculator
Like a cone, a pyramid occupies one third of the prism around it. The slant height is measured from the middle of a base edge to the apex and drives the triangular faces; the lateral edge runs from a base corner to the apex and is the longer of the two, since it cuts across the base diagonally.
Worked example
calculated with the default values below
Base side length 6 · Height 10 Volume 120.000 unit³ · Base area 36.000 unit² · Slant height 10.4403 unit · Lateral edge length 10.8628 unit · Lateral surface area 125.284 unit² · Total surface area 161.284 unit²
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
V = s²h ÷ 3; l = √(h² + (s ÷ 2)²); A_lat = 2sl; e = √(h² + s² ÷ 2)
- s
- Base side
- h
- Height
- V
- Volume
- l
- Slant height
- A_lat
- Lateral area
- e
- Lateral edge
Regular square pyramid. Base area = s²; total surface area = s² + 2sl.
Frequently asked questions
What dimensions does this calculator use?
It models a right square pyramid. Enter the side length of the square base and the perpendicular height, using the same unit for both. The volume is base area × height ÷ 3. Results are in cubic units.
What assumptions does the calculator make?
It assumes the apex is directly above the centre of the square base. The slant height runs from the midpoint of a base edge to the apex; a lateral edge runs from a base corner to the apex. The surface-area results use this same centred geometry, so the calculator does not model other base shapes or an off-centre apex.