How to use the regular polygon calculator
- Enter the whole number of sides from 3 through 1000.
- Enter the common side length as a positive number; do not add a unit symbol.
- Calculate to see area, perimeter, one interior angle, apothem/inradius and circumradius.
- Editing either input clears the old result and copy state.
Regular polygon formulas
A regular polygon has equal sides and equal interior angles. Its perimeter is P=ns and each interior angle is (n−2)×180°/n.
Splitting the polygon into n congruent central triangles gives apothem rᵢ=s/(2tan(π/n)) and area A=Prᵢ/2=ns²/(4tan(π/n)).
The center-to-vertex circumradius is r𝒸=s/(2sin(π/n)). Trigonometric functions use radians internally; ordinary displays use at most two decimals.
Worked examples
Regular hexagon, side 4
n=6 and s=4 give perimeter 24, area 24√3 ≈ 41.57, interior angle 120°, inradius 2√3 ≈ 3.46 and circumradius 4.
Square, side 5
n=4 and s=5 give perimeter 20, area 25, interior angle 90°, inradius 2.5 and circumradius 5/√2 ≈ 3.54.
Limits and input rules
- Sides must be an integer from 3 to 1000; decimals and fewer than three sides are rejected.
- The formulas assume a convex regular polygon, not an irregular or self-intersecting shape.
- Changing the interpreted length unit does not change the number; this page performs no unit conversion.
- At high side counts the polygon approaches a circle, but the answer remains the exact regular n-gon model.
Frequently asked questions
Is the apothem the inradius?
Yes. For a regular polygon it reaches the midpoint of a side and is the incircle radius.
What is the circumradius?
It runs from the center to a vertex and is the radius of the circle through all vertices.
Can I use unequal sides?
No. This page deliberately models regular polygons only.