Calculate volume and surface area of a regular square pyramid.
The Pyramid Area Calculator is a geometric tool designed to calculate the surface area of a pyramid. A pyramid is a three-dimensional polyhedron formed by connecting a polygonal base to a single point called the apex. The most common type is a regular square pyramid, which has a square base and four congruent isosceles triangular faces. The parameters defining a square pyramid are its base edge (a), vertical height (h), and slant height (s) of the triangular faces.
The total surface area (A_total) of a pyramid is the sum of its base area (A_base) and its lateral surface area (A_lateral). For a square pyramid with base edge a, the base area is A_base = a². The lateral surface area consists of four triangles, each with an area of 1/2 × base × height, resulting in A_lateral = 4 × (1/2 × a × s) = 2as. The total surface area is therefore: A_total = a² + 2as. If the slant height is not known but the vertical height (h) is given, the slant height can be calculated using the Pythagorean theorem: s = √((a/2)² + h²).
Pyramid surface area calculations are used in architecture, structural engineering, and packaging design to estimate the materials required to construct or cover pyramid structures. The pyramid area calculator automates these multi-step computations, providing instant results for base, lateral, and total surface area, ensuring accuracy in design planning.
Square Pyramid Math
A square pyramid consists of a square flat base with triangular side faces meeting at the apex.
- Volume (V):
V = 1/3 × Base Area × Height = 1/3 × b² × h - Slant Height (s):
s = √( (b/2)² + h² ) - Surface Area (A):
A = Base Area + 4 × Lateral Triangle Areas = b² + 2bs
How it Works & Formula
Calculates the volume of a square pyramid.
Practical Examples
Base side 230m, height 146m: Volume = ⅓ × (230²) × 146 ≈ 2,574,466 m³.
Frequently Asked Questions
How do you find the surface area of a pyramid?
Add the base area to the sum of the areas of the triangular faces (lateral area).