Case 1
- Number of sides
- 6
- Length of one side
- 4
41.569219
Open with these valuesRegular Polygon Area Calculator
Change any value to update the result.
41.569219units²
Polygon area: 41.569219 units²Examples
How the result moves
Length of one side → Polygon area (units²)Your current valid inputs, with one value varied across the range.
How the result moves
Held fixed: Number of sides 6.
| Length of one side | Polygon area |
|---|---|
| 2.000 | 10.392305 |
| 4.000Your value | 41.569219 |
| 6.000 | 93.530744 |
| 8.000 | 166.276878 |
Works for any regular shape from a triangle upward: n × s² ÷ (4 tan(π ÷ n)). All sides must be equal — for an irregular shape, split it into triangles instead. More sides at the same side length always means more area.
Worked examples
Case 2
- Number of sides
- 3
- Length of one side
- 1
0.433013
Open with these valuesCase 3
- Number of sides
- 8
- Length of one side
- 3
43.455844
Open with these valuesHow it's calculated
A = n × s² ÷ (4 × tan(π ÷ n))
- StepEnter how many sides the shape has, at least three.Number of sides=6
- StepEnter the length of one side — all of them are equal.Length of one side=4
- ResultRead the area in the square of that unit.41.569219units²
Reference table
| Sides, side length | Shape | Area |
|---|---|---|
| 3, 1 | triangle | 0.433013 |
| 5, 2 | pentagon | 6.881910 |
| 4, 5 | square | 25.000000 |
| 6, 4 | hexagon | 41.569219 |
| 8, 3 | octagon | 43.455844 |
Questions
How do you find the area of a regular polygon?
Square the side, multiply by the number of sides, then divide by four times the tangent of π ÷ n. A hexagon with side 4 covers about 41.57 square units.
Does this work for irregular shapes?
No. It assumes every side and every angle is the same. An irregular polygon has to be split into triangles and added up.
Why does the square case not come out exactly 25?
It does mathematically — tan(45°) is exactly 1. In floating point it lands on 25.000000000000004, and the calculator reports the value it actually computes rather than tidying it.
What happens with many sides?
The shape approaches a circle. At a hundred sides it is already within a hundredth of a per cent of the circle with the same perimeter.