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Regular Polygon Apothem from Side and N Calculator

a = s / (2 · tan(π / n)).

Compute the apothem (perpendicular distance from the centre to the midpoint of a side) of a regular n-sided polygon with side length s: a = s / (2 · tan(π / n)). Apothem = inscribed-circle radius. Used to compute polygon area A = ½ · a · perimeter and the inscribed-circle area.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

a = s / (2 · tan(π / n)).

In depth

Compute the apothem (perpendicular distance from the centre to the midpoint of a side) of a regular n-sided polygon with side length s: a = s / (2 · tan(π / n)). Apothem = inscribed-circle radius. Used to compute polygon area A = ½ · a · perimeter and the inscribed-circle area.