Calculators
Regular Polygon Calculator
Calculate area, perimeter, apothem, circumradius, and interior angle from the side length of a regular polygon.
Calculate measurements of an equal-sided, equal-angle polygon.
For n sides of length s, perimeter P = ns, apothem a = s / (2 tan(π/n)), area A = Pa/2, circumradius R = s / (2 sin(π/n)), and each interior angle is 180 − 360/n degrees. For a regular hexagon with side length 10, perimeter is 60 and area is approximately 259.807621 square units. The apothem runs from the center to the midpoint of a side; the circumradius runs to a vertex. Enter 3 to 10000 sides and a side length from 1e-100 to 1e100. These formulas apply only to convex regular polygons. Length results use your input unit; area uses its square. Results are rounded to 12 significant digits using browser floating-point arithmetic. Everything runs locally in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What makes a polygon regular?
A regular polygon has equal side lengths and equal interior angles. This calculator handles convex regular polygons, including equilateral triangles, squares, and regular hexagons.
How is polygon area calculated?
Area equals half the perimeter times the apothem: A = ns² / (4 tan(π/n)). The tangent uses radians. A square with side length 10 has area 100 square units.
What is the difference between apothem and circumradius?
The apothem is the perpendicular distance from the center to a side. The circumradius is the distance from the center to a vertex.
Can I use this for an irregular polygon?
No. Side count and one side length do not determine the area of an irregular polygon.
Which units should I enter?
Use any consistent length unit. A length entered in meters produces perimeter and radii in meters and area in square meters. No unit conversion is performed.