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Polygon Interior Angle Calculator

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

About Polygon Interior Angle Calculator

Any n-gon can be cut into n − 2 triangles from a single vertex, so its interior angles total (n − 2) × 180°. Dividing by n gives each angle of a regular polygon.

Formulas

Interior angle sum

Σ = (n − 2) × 180°

Each interior angle (regular)

θ = (n − 2) × 180° / n

Worked example

With the default values below, Polygon Interior Angle Calculator returns Each interior angle (regular) of 135.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of sidesaccepts 3–1,000
8
Known interior angles total so farminimum 0 °
900 °

Results

Each interior angle (regular)
135.0000 °
Sum of interior angles
1,080 °
Each exterior angle (regular)
45.0000 °
Remaining angle total
180.0000 °

Step by step

  1. 1Values used
  2. 2Interior angle sum
  3. 3Each interior angle (regular)
  4. 4Each interior angle (regular)= 135.0000 °
  5. 5Sum of interior angles= 1,080 °
  6. 6Each exterior angle (regular)= 45.0000 °
  7. 7Remaining angle total= 180.0000 °

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

What is the interior angle of a regular hexagon?

(6 − 2) × 180° / 6 = 120°.

Why does interior + exterior equal 180°?

They form a linear pair along the extended side, so they are supplementary.

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Polygon Interior Angle Calculator | Calcrivo