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Polygon Exterior Angle Calculator

Work out polygon exterior angle instantly with clear inputs, formula shown and shareable results.

About Polygon Exterior Angle Calculator

Walking once around any convex polygon you turn through a full revolution, so the exterior angles always total 360°. For a regular polygon each turn is therefore 360°/n.

Formula

Exterior angle

θ = 360° / n, and Σ exterior = 360° for every convex polygon

Worked example

With the default values below, Polygon Exterior Angle Calculator returns Each exterior angle of 36.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of sidesaccepts 3–1,000
10
Number of vertices walkedminimum 1
3

Results

Each exterior angle
36.0000 °
Sum of exterior angles
360 °
Each interior angle
144.0000 °
Total turn after the vertices walked
108.0000 °

Step by step

  1. 1Values used
  2. 2Exterior angle
  3. 3Each exterior angle= 36.0000 °
  4. 4Sum of exterior angles= 360 °
  5. 5Each interior angle= 144.0000 °
  6. 6Total turn after the vertices walked= 108.0000 °

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does the 360° total depend on the number of sides?

No. That is the striking part: a triangle and a 100-gon both have exterior angles totalling 360°.

How do I find n from an exterior angle?

n = 360° ÷ exterior angle. An exterior angle of 24° means 15 sides.

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