Octagonal Prism Calculator

What is an Octagonal Prism?

An octagonal prism is a three-dimensional polyhedron consisting of two octagonal bases (top and bottom) and eight rectangular lateral faces connecting them. In a regular right octagonal prism, both bases are regular octagons, and all lateral faces are congruent rectangles meeting the bases at right angles. For other geometric calculations, try the Octagon Calculator, Octahedron Calculator, and Volume Calculator.

Essential Octagonal Prism Formulas

To calculate the geometric properties of a regular right octagonal prism, you need the base edge length $a$ and the height (or length) of the prism $L$.

• Base Area ($A_b$): The area of one octagonal base: $$A_b = 2(1 + \sqrt{2})a^2 \approx 4.828427 a^2$$
• Lateral Surface Area ($A_l$): The surface area of the eight side faces: $$A_l = 8aL$$
• Total Surface Area ($S$): The sum of the base areas and the lateral area: $$S = 2A_b + A_l = 4(1 + \sqrt{2})a^2 + 8aL \approx 9.656854 a^2 + 8aL$$
• Volume ($V$): The amount of space enclosed by the prism: $$V = A_b L = 2(1 + \sqrt{2})a^2 L \approx 4.828427 a^2 L$$

Bidirectional Calculations

Our calculator allows you to solve for any missing value. If you know the volume and height, you can solve for the base side length. If you know the total surface area and base side length, you can calculate the height. This is incredibly useful for design engineering, architectural drafting, and spatial geometry problems.