Regular Polygon Calculator
Calculate properties of any regular polygon (3–100 sides) including area, angles, apothem, and circumradius.
Dimensions
Updates as you typePreset (sets n)
Solve from
Which measurement do you know? ?
Measurements
Number of sides (n) ?
hexagon
sides
Side length (s) ?
cm
—
Shape
Compare polygons at the same side length
n = 3 → 20| Shape | n | Perimeter | Area | Apothem | Circumradius | Area vs. circle |
|---|---|---|---|---|---|---|
| Enter a side length to see the comparison. | ||||||
Formula
A
=
n · s²
4 · tan(π / n)
P
=
n · s
a
=
s
2 · tan(π / n)
R
=
s
2 · sin(π / n)
- A
- Area of the polygon
- P
- Perimeter — sum of all n sides
- n
- Number of sides (n ≥ 3)
- s
- Side length — all sides are equal in a regular polygon
- a
- Apothem — center to midpoint of a side (inscribed-circle radius)
- R
- Circumradius — center to any vertex (circumscribed-circle radius)
- Interior angle
- (n − 2) · 180° / n
- Exterior angle
- 360° / n — also the central angle subtended by one side
Worked example — your numbers
- n = —, s = —
- π / n = —
- tan(π / n) = —
- Area = n · s² / (4 · tan(π/n)) = —
- Perimeter = n · s = —
- Apothem = s / (2 · tan(π/n)) = —
- Circumradius = s / (2 · sin(π/n)) = —
A regular polygon is n congruent isosceles triangles glued around a common center — which is why the area formula reduces to n triangles each with base s and height a (the apothem). As n grows the polygon tends to a circle: at n = 100 the apothem and circumradius agree to within 0.05%.