Regular Polygon Perimeter Calculator
A regular polygon is a flat shape with every side the same length and every interior angle equal, from the equilateral triangle and square through the pentagon, hexagon and beyond. Because all sides are equal, the perimeter is just the number of sides multiplied by one side length. This tool returns the perimeter, the exact enclosed area, and the interior angle at each corner. Enter how many sides the polygon has and how long each side is, both as ordinary numbers, and the results update instantly. The perimeter and side length share the same unit.
Regular polygon perimeter formula
Perimeter = n * s
Area = (1 / 4) * n * s^2 * cot(pi / n)
Interior angle = (n - 2) * 180 / n degrees
Here n is the number of equal sides and s is the length of one side. The cotangent term in the area formula is exact for any whole side count of three or more.
How regular polygon perimeter works
- Because every side is equal, the perimeter is simply the side count times one side length.
- A regular polygon needs at least three sides, so side counts below three are treated as invalid.
- The side count must be a whole number; a polygon cannot have a fractional number of sides.
- The interior angle grows toward 180 degrees as the side count rises, approaching a circle.
- The perimeter shares the unit of the side length, and the area uses the corresponding square units.
Regular polygon perimeter: frequently asked questions
What is the formula for the perimeter of a regular polygon?
A regular polygon has all sides equal, so its perimeter is simply the number of sides times the length of one side: P = n * s, where n is the side count and s is the side length. A regular pentagon with 5 sides each 4 units long has a perimeter of 5 times 4, which equals 20 units.
What counts as a regular polygon?
A regular polygon is a flat shape with all sides of equal length and all interior angles equal. Examples include the equilateral triangle, square, regular pentagon, regular hexagon and so on. Irregular polygons, where sides differ, do not use this simple multiplication formula and must have each side added individually.
Does this calculator also give the area?
Yes. Using the side length and side count it computes the exact area with the formula A = (1/4) * n * s^2 * cot(pi/n), where cot is the cotangent. This is the standard closed-form area of a regular polygon and is exact for any number of sides of three or more.
What is the minimum number of sides?
A polygon must have at least three sides, since you cannot enclose an area with two straight segments. This calculator treats any side count below three as invalid. The side count should also be a whole number, because a polygon cannot have a fractional number of sides.
What units does the perimeter use?
The perimeter is in the same length unit as the side length you enter. If the side is in metres, the perimeter is in metres. The area is reported in the corresponding square units. There is no unit mixing, so the result follows directly from your input.
Official sources
- National Institute of Standards and Technology: Digital Library of Mathematical Functions: trigonometric functions.
- National Institute of Standards and Technology: SI Units and measurement.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.