Regular Polygon Calculator

Calculate key dimensions of a regular polygon

Your result will appear here.

About the Regular Polygon Calculator

Regular Polygon Calculator works with shapes whose sides and interior angles are all equal. From side length and number of sides, it can derive perimeter, area, interior angle and related measurements.

As the number of sides increases while the polygon remains regular, its shape approaches a circle. The formulas depend on equal side lengths and equal angular spacing around the centre.

How to Use the Regular Polygon Calculator

  1. Enter the number of sides.
  2. Enter side length or another supported dimension.
  3. Calculate perimeter, area or angles.
  4. Verify the polygon is regular before applying the equal-side formulas.

How the Calculation Works

For a regular polygon with n sides of equal length s, perimeter P = n×s. The equal central angle is 360°/n, while each interior angle is (n−2)×180°/n because the sum of all interior angles is (n−2)×180°.

Area can be calculated as A = n s²/[4 tan(π/n)]. An equivalent form is A = perimeter×apothem/2, where the apothem is the perpendicular distance from the polygon centre to the midpoint of a side. Both forms assume a truly regular polygon with equal sides and equal angles.

Worked example

Regular Polygon Calculator Worked Example

Regular hexagon with side 5 cm

Perimeter = 6×5 = 30 cm. Area = 6×25/[4 tan30°] ≈ 64.95 cm².

Result guide

Understanding Your Regular Polygon Calculator Result

The formulas apply only when every side and angle is equal. An irregular six-sided polygon can have the same perimeter but a very different area. The apothem can also be used to calculate area as A = perimeter×apothem/2. That form is useful when the side length is not known directly but the centre-to-side distance is available from a drawing or layout.

Before you rely on the answer

Assumptions and Limitations

  • Number of sides is an integer of at least three.
  • All sides are equal.
  • Angles follow regular-polygon geometry.

Practical tip

Using This Result in Practice

If you know the distance from centre to side or vertex instead of side length, use the corresponding apothem or circumradius relationship rather than forcing a side-length estimate.

Related calculations

Useful Calculations to Continue With

If the shape is irregular or composite, use the Area Calculator instead of regular-polygon formulas.

If the number of sides is effectively being replaced by a circular boundary, use the Circle Calculator.

Common questions

Regular Polygon Calculator FAQ

What is the perimeter of a regular polygon?

Number of sides multiplied by side length.

How do I find one interior angle?

Use (n−2)×180°/n.

Can these formulas be used for irregular polygons?

No. They assume equal sides and equal angles.