Calculators
Octagonal Pyramid Calculator
Calculate right regular octagonal pyramid volume, base and surface areas, slant height, and lateral edge length privately in your browser.
Measure a right pyramid with a regular octagonal base.
A right regular octagonal pyramid has one regular octagonal base and eight triangular faces, with its apex directly above the base center. Enter base side a and perpendicular height h in the same length unit. Base area B = 2(1 + √2)a²; perimeter P = 8a; apothem r = a/[2 tan(π/8)]; circumradius R = a/[2 sin(π/8)]. 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 is approximately 19.313708499 square units and volume is 19.313708499 cubic units. Slant height reaches a side midpoint; 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 calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I calculate octagonal pyramid volume?
Calculate base area B = 2(1 + √2)a², then volume V = Bh/3. Side 2 and perpendicular height 3 give approximately 19.313708499 cubic units.
Does total surface area include the base?
Yes. Total area is B + Ps/2, where P = 8a and s is face slant height. Lateral area Ps/2 includes only the eight triangular faces.
How do slant height and lateral edge differ?
Slant height √(h² + r²) reaches a base side midpoint. Lateral edge √(h² + R²) reaches a base vertex. Enter perpendicular height, not either of these sloping lengths.
Which shapes and inputs are supported?
Use a regular octagonal base with the apex directly above its center. Enter side and perpendicular height from 1e-50 to 1e50 using one consistent length unit. Scientific notation is accepted. Irregular bases and off-center apexes are not supported. Processing stays in your browser.