Calculators
Octagonal Prism Calculator
Calculate right regular octagonal prism volume, base area, lateral and total surface area, apothem, and circumradius privately in your browser.
Measure a right prism with a regular octagonal base.
A right regular octagonal prism has two identical regular octagonal bases and eight rectangular side faces. Enter base side a and perpendicular height h in the same length unit. One base area B = 2(1 + √2)a²; base perimeter P = 8a; volume V = Bh; lateral area L = Ph; total surface area A = 2B + L. Base apothem r = a/[2 tan(π/8)] and circumradius R = a/[2 sin(π/8)]. The apothem reaches a side midpoint; the circumradius reaches a vertex. For a = 2 and h = 5, one base area is approximately 19.313708499 square units, volume is 96.5685424949 cubic units, and total area is 118.627416998 square units. These formulas require a regular octagon and a right prism; they do not describe an irregular or oblique prism. 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 prism volume?
For a regular octagonal base of side a, base area B = 2(1 + √2)a². Multiply B by perpendicular height h to get volume. Side 2 and height 5 give approximately 96.5685424949 cubic units.
Does total surface area include both bases?
Yes. Total surface area is 2B + 8ah. Lateral area 8ah includes only the eight rectangular side faces.
What is the difference between apothem and circumradius?
The apothem reaches a base side midpoint and equals a/[2 tan(π/8)]. The circumradius reaches a base vertex and equals a/[2 sin(π/8)]. Enter the base side length, not either radius.
Which inputs and shapes are supported?
Use a right prism with regular octagonal bases. Enter positive side and perpendicular height from 1e-50 to 1e50 in one consistent length unit. Scientific notation is accepted. Irregular and oblique prisms are not supported. Results are rounded to 12 significant digits in your browser.