Calculators

Pentagonal Pyramid Calculator

Calculate right regular pentagonal pyramid volume, base and surface areas, slant height, and lateral edge length privately in your browser.

Enter a regular pentagonal base side and perpendicular pyramid height. The apex must lie directly above the base center. Slant height runs to a side midpoint; lateral edges run to base vertices. Use one consistent length unit, from 1e-50 to 1e50.

Measure a right pyramid with a regular pentagonal base.

A right regular pentagonal pyramid has one regular pentagonal base and five triangular faces, with its apex directly above the base center. Enter base side a and perpendicular height h using the same length unit. Base area B = √(25 + 10√5)a²/4; perimeter P = 5a; apothem r = a/[2 tan(π/5)]; circumradius R = a/[2 sin(π/5)]. Face slant height s = √(h² + r²) and lateral edge e = √(h² + R²). Volume V = Bh/3; lateral area L = Ps/2; total surface area A = B + L. For a = 2 and h = 3, base area and volume are approximately 6.88190960236 square and cubic units respectively. Slant height reaches a side midpoint, while a lateral edge reaches a vertex. These formulas require a regular base and centered apex. Use positive lengths from 1e-50 to 1e50; scientific notation is accepted. Areas use square units and volume uses cubic units. Results use browser floating-point arithmetic rounded to 12 significant digits. All inputs stay in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

How do I calculate pentagonal pyramid volume?

Use V = Bh/3, where B = √(25 + 10√5)a²/4 for regular base side a. Side 2 and perpendicular height 3 give approximately 6.88190960236 cubic units.

Does total surface area include the base?

Yes. Total area is B + 5as/2, where s is the face slant height. Lateral area 5as/2 includes only the five triangular faces.

How is slant height different from lateral edge length?

Slant height runs from the apex to a base side midpoint: s = √(h² + r²), with apothem r = a/[2 tan(π/5)]. A lateral edge reaches a base vertex: e = √(h² + R²), with circumradius R = a/[2 sin(π/5)]. Neither is the perpendicular height.

Which inputs and shapes are supported?

Use a regular pentagonal base with the apex directly above its center. Enter positive side and perpendicular height from 1e-50 to 1e50 in one unit. Scientific notation is accepted. Irregular or oblique pyramids are not supported. Results are rounded to 12 significant digits locally in your browser.