Regular Polygon Area Calculator
From the number of sides and one side length, get the perimeter, the apothem, and the area — the three numbers that describe any regular polygon.
Two inputs, three answers
Enter the number of sides and the side length and the calculator returns the perimeter (n × s), the apothem (s/(2·tan(π/n))), and the area (½ × perimeter × apothem) at once.
Regular polygons only
These formulas assume a regular polygon — every side equal, every angle equal. If the sides or angles differ, split the shape into triangles instead.
What is a regular polygon area calculator?
Sides and length in, full polygon out
A regular polygon area calculator turns two measurements — how many equal sides the shape has and how long each side is — into the numbers that describe a whole regular polygon: the distance around it (perimeter), the distance from its centre to the middle of a side (apothem), and the space it encloses (area). Because every side and every angle is equal, those two inputs fix the shape completely. That makes it all you need for an equilateral triangle (3 sides), a square (4), a regular hexagon (6), or any tiling, nut, bolt head, or geometry homework where a regular polygon shows up.
Enter the number of sides and one side length to get the perimeter, apothem, and area instantly.
A regular polygon has equal sides and equal angles, so three short formulas built from the number of sides n, the side length s, and the constant π describe it completely.
area = ½ × perimeter × apothemThe perimeter is simply n × s, the total distance around. The apothem is the distance from the centre to the middle of a side — the radius of the largest circle that fits inside — and equals s / (2 × tan(π/n)). Multiply half the perimeter by the apothem and you get the area: ½ × perimeter × apothem.
Suppose you have a regular hexagon (6 sides) with a side length of 4.
Perimeter
6 × 4 = 24 — the total distance around the hexagon.
Apothem
4 / (2 × tan(π/6)) = 4 / (2 × 0.577350) ≈ 3.464102 — centre to side midpoint.
Area
(24 × 3.464102) ÷ 2 ≈ 41.569219 square units — the space enclosed.
The three outputs answer three different practical questions. The perimeter (24 for a hexagon with side 4) is how much edge you would walk, fence, or frame — the distance once around. The apothem (about 3.464102 here) is the distance from the centre straight out to the middle of a side; it is the radius of the biggest circle that fits inside the polygon, which is why it matters for nuts, bolt heads, and anything that must seat against a flat. The area (about 41.569219 square units) is the space enclosed — the material to cut, the floor to tile, the surface to paint. The single most useful insight is the link to a circle: as you add sides while keeping the shape the same size, the polygon's outline gets smoother and its area creeps toward the area of a circle. An equilateral triangle (3 sides) is the leanest regular polygon, a square (4) the most familiar, and a hexagon (6) the one nature reaches for in honeycombs because it tiles a plane with no gaps. Keep in mind that all three results assume a truly regular polygon — equal sides and equal angles throughout.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular polygons and consistent units
These formulas describe a perfect regular polygon — every side the same length and every interior angle equal. An irregular polygon (sides or angles that differ) will not match the computed value; for those, split the shape into triangles and add their areas. The side length is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a side length in centimetres gives a perimeter and apothem in centimetres and an area in square centimetres, never a mix.