Regular Polygon Area CalculatorFree online math calculator — instant results, no sign-up
Calculate a regular polygon's area from its side length.
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About the Regular Polygon Area Calculator
The Regular Polygon Area Calculator finds the area enclosed by a regular polygon using its number of sides and side length. It assumes all sides and all interior angles are equal. With the default inputs of 7 sides and a side length of 5, the result is 90.8478111 square units.
- Number of sides
- The unitless count of the polygon's sides must be a whole number of at least 3; the default is 7.
- Side length
- The length of each equal side must be positive and expressed in a consistent length unit, such as centimeters or meters; the default is 5.
Formula and method
A = n × s² / [4 × tan(π / n)]; with n = 7 and s = 5, A = 7 × 5² / [4 × tan(π / 7)] ≈ 90.8478111.
- AArea of the regular polygon, in square units.
- nNumber of sides, a whole number of at least 3.
- sLength of each side, in the chosen length unit.
- πPi, the mathematical constant approximately equal to 3.141592653589793.
- tanThe tangent function, evaluated with its angle in radians.
The polygon can be divided into n congruent triangles meeting at its center. Each triangle has base s and height equal to the apothem, s / [2 × tan(π / n)]. Adding the triangle areas gives A = n × s² / [4 × tan(π / n)]. For the default inputs, the numerator is 7 × 25 = 175 and the denominator is 4 × tan(π / 7), producing approximately 90.8478111 square units.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Number of sides7
- Side length5
Results
- Result90.8478111
How to use the Regular Polygon Area Calculator
- 1Confirm that the polygon is regular: all sides and all interior angles must be equal.
- 2Enter the Number of sides as a whole number of at least 3; leave it at 7 for the worked example.
- 3Enter the Side length in your chosen length unit; leave it at 5 for the worked example.
- 4Run the calculation to evaluate A = n × s² / [4 × tan(π / n)].
- 5Read the Result as an area in squared length units; the default inputs give 90.8478111 square units.
Reading your result
The Result row reports the area enclosed by the regular polygon, not its perimeter or side length. For 7 sides of length 5, Result = 90.8478111 square units. If the side length is in centimeters, the area is in square centimeters; if it is in meters, the area is in square meters.
Limitations
This formula applies to simple, non-self-intersecting regular polygons in a flat plane. It does not determine the area of an irregular polygon from a side count and one side length, and equal side lengths alone do not guarantee that a polygon is regular. The number of sides must be an integer of at least 3, and the side length must be positive. The displayed result is a rounded numerical approximation; its digits do not imply greater precision than the side-length measurement supports.
Common questions
Why do 7 sides of length 5 give an area of 90.8478111?+
Substituting n = 7 and s = 5 into A = n × s² / [4 × tan(π / n)] gives 175 / [4 × tan(π / 7)] ≈ 90.8478111 square units. The tangent angle must be evaluated in radians.
Can I use this calculator for a polygon with equal sides but unequal angles?+
No. The formula assumes both equal sides and equal interior angles. A polygon with equal sides but unequal angles generally needs additional measurements to determine its area.
Do I need to measure the apothem or radius?+
No. For a regular polygon, the side count and side length determine the apothem through s / [2 × tan(π / n)], so no separate apothem or radius input is needed.
How does changing the side length affect the area if the number of sides stays fixed?+
Area is proportional to the square of the side length. Multiplying every side length by a factor multiplies the area by the square of that factor, provided the polygon remains regular and its side count is unchanged.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.