Calculators
Pentagonal Prism Calculator
Calculate regular pentagonal prism volume, base area, lateral and total surface area, apothem, and circumradius privately in your browser.
Measure a right prism with a regular pentagonal base.
A right regular pentagonal prism has two identical regular pentagonal bases and five rectangular side faces. Enter base side a and perpendicular height h in the same length unit. One base area B = √(25 + 10√5)a²/4; base perimeter P = 5a; volume V = Bh; lateral area = Ph; total surface area = 2B + Ph. Base apothem r = a/[2 tan(π/5)] and circumradius R = a/[2 sin(π/5)]. The apothem runs from the base center to a side midpoint; the circumradius runs to a vertex. For a = 2 and h = 5, base area is approximately 6.88190960236 square units, volume is 34.4095480118 cubic units, and total surface area is 63.7638192047 square units. These formulas require a regular pentagon and a right 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 pentagonal prism volume?
Multiply the regular pentagonal base area by perpendicular height: V = √(25 + 10√5)a²h/4. Side 2 and height 5 give approximately 34.4095480118 cubic units.
Does surface area include both bases?
Yes. Total surface area is 2B + 5ah, where B is one pentagonal base area. Lateral area 5ah includes only the five rectangular side faces.
What are the apothem and circumradius?
The apothem is the distance from the base center to a side midpoint, a/[2 tan(π/5)]. The circumradius reaches a vertex, a/[2 sin(π/5)]. Enter a side length rather than either radius.
Which inputs and shapes are supported?
Use a right prism with a regular pentagonal base and positive lengths from 1e-50 to 1e50 in a consistent unit. Scientific notation is accepted. Irregular bases and oblique prisms are not supported. Results are rounded to 12 significant digits and calculated locally in your browser.