⬟ Pentagon Area Calculator

What this calculator does

This tool finds the area, perimeter, and apothem of a regular pentagon (a five-sided polygon with all sides and angles equal) from a single measurement: the length of one side.

The formula

For a regular pentagon with side length s, the area is A = (1/4) × √(5(5 + 2√5)) × s², a standard result derived from splitting the pentagon into five equal triangles from its center. The perimeter is 5 × s, and the apothem (distance from the center to the middle of a side) is s / (2 × tan(36°)).

• Works for any unit of length – just keep your input consistent.
• Only valid for regular pentagons, where every side and angle is equal.

This tool is intended for general math, design, and educational planning purposes.