Free · 2D geometry calculators 📏

Regular Polygon Interior and Turning Angles

It is the nonreflex turning angle 360°/n, supplementary to the interior angle. It is not the reflex angle outside the polygon.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Number of sides 6 gives Interior angle α 120, Exterior turning angle β 60.

α = (n−2)π/n; β = 2π/n

Worked example

Enter these known values and leave the other values blank.

Number of sides
6
Interior angle α
120 deg
Exterior turning angle β
60 deg

Assumptions and limitations

  • For a convex regular polygon, α is the interior angle and β is the exterior turning angle at a vertex. They add to 180 degrees. Whole n is at least three; a supplied angle must imply such a side count. This is not the angle at every vertex of an arbitrary polygon.
  • Clear unknown measurements before solving backward. Use compatible units and independent values. Reference pictures are original schematic drawings. Independently rounded measurements can fail strict compatibility at a boundary.

Common questions

Which exterior angle is reported?

It is the nonreflex turning angle 360°/n, supplementary to the interior angle. It is not the reflex angle outside the polygon.

How do I use this calculator with different units?

Select the unit beside each measure. Length, squared length and volume use different dimensions; changing a unit preserves the physical value. Compound length controls represent feet/inches or meters/centimeters together.

References

Snap only angle-derived side counts within 1e-40 of a whole number to that integer, preventing finite-precision π cancellation from rejecting exact regular-pentagon angles; other fractional counts remain invalid.

Explore 2d geometry calculators 📏 or browse all math calculators.