Polygon Angle Calculator

Created by Michael Darcy
Reviewed by Rahul Dhari
Last updated: Aug 28, 2022

If you want to calculate the interior and exterior angles of polygons that are regular, the polygon angle calculator can help you. Enter the numbers straight away or read on to learn how to calculate angles in a polygon.
If you're unfamiliar with the difference between the interior and exterior angles of polygons, don't worry - we'll cover that too!

Interior and exterior angles of polygons

Before we learn how to calculate angles in a polygon, it's worth knowing what exactly we can determine. The two most important types are:

  • Interior polygon angles - These lie inside the polygon at its vertices.
  • Exterior polygon angles - They are defined outside the polygon between one of its sides and the extension of an adjacent side.

In regular polygons whose sides all have the same length, the angles of the same type are equal.

How to find the interior angle of a polygon?

For a regular polygon with nn sides, the interior angle, α\alpha, can be found using the formula:

α=(n2)πn.\alpha = \frac{(n - 2)\pi}{n}.

🔎 The numerator in this formula gives you the sum of interior angles in a polygon.

Formula to calculate the exterior angle of a polygon

You can calculate the exterior angle of a polygon, β\beta, using the following equation:

β=2πn.\beta = \frac{2\pi}{n}.

It may be helpful to remember that the exterior and interior polygon angles sum up to 180°. Therefore, you can write:

β=2πα,\beta = 2\pi - \alpha,

where we used the fact that 2π=180°2\pi = 180\degree. Feel free to brush up on the angle conversion if there's any confusion! Both radians and degrees are fine to use but remember to keep the units consistent.
You can also save yourself the hassle and use the polygon angle calculator, which allows easy conversion between the units.

Other calculators about polygons

If you'd like to do more than calculate the interior and exterior angles of polygons, we've got plenty of tools that can assist you:

FAQ

How do I find the interior angle of a regular polygon?

You can calculate the interior angles of a regular polygon as follows:

  1. Determine the number of sides, n.
  2. Subtract 2 from n.
  3. Multiply the difference by π.
  4. Divide the result by n - this is the magnitude of the interior polygon angles.

What regular polygon has an exterior angle of 60 degrees?

A regular hexagon has an exterior angle of 60°. Exterior angles always sum up to 360°. Dividing it by 60° gives 6 - the number of sides in a hexagon.

How many angles does a regular polygon have?

Regular polygons have as many angles as sides, both interior and exterior. For example, a pentagon has 5 sides, 5 interior angles, and 5 exterior angles.

Which regular polygon will have the largest angle measure?

An equilateral triangle has the largest exterior angle, 120°.
For an interior angle, the limit is 180°, which is approached as the number of sides tends to infinity.

Michael Darcy
Number of sides
Name
Parameters
α
deg
β
deg
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