Home›Math›Pyramid Calculator

Pyramid Calculator (Square Base)

Calculate volume, surface area, slant height, and lateral edge of a right square pyramid. Like the Egyptian pyramids.

Calculator

Base Side (a)

Height (h)

Square Pyramid Diagram

Pyramid Formulas

Volume & Base:

Volume: V = ⅓a²h
Base Area: A = a²
Base Diagonal: d = a√2

Heights & Surface:

Slant Height: s = √(h² + (a/2)²)
Lateral Edge: l = √(h² + a²/2)
Lateral Area: LA = 2as
Total Area: SA = a² + 2as

Understanding Square Pyramids

A square pyramid has a square base and four triangular faces meeting at an apex. The most famous examples are the Egyptian pyramids of Giza.

Key Properties:

5 faces: 1 square base + 4 triangular lateral faces
8 edges: 4 base edges + 4 lateral edges
5 vertices: 4 base corners + 1 apex
Volume is ⅓ of a prism with the same base and height

Frequently Asked Questions

What's the difference between slant height and lateral edge?

Slant height goes from the apex to the middle of a base edge (perpendicular to it). Lateral edge goes from apex to a corner of the base. The lateral edge is always longer.

How tall is the Great Pyramid of Giza?

Originally about 146.5 m (481 ft), now about 138.5 m due to erosion. Base side is 230.4 m. Using our formulas: V ≈ 2.6 million m³, slant height ≈ 186.4 m.

Why is the volume formula ⅓?

This can be proven with calculus or by showing that 3 identical pyramids can fill a cube (when each pyramid has its apex at the cube center and base on a cube face).

Related Calculators

Triangular Pyramid Cone Frustum Tetrahedron

Loading Calculator...

Please wait a moment