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Pentagon Area Calculator

Work out pentagon area instantly with clear inputs, formula shown and shareable results.

About Pentagon Area Calculator

A regular pentagon has 5 equal sides. Splitting it into 5 isosceles triangles from the centre gives A = 5s² / (4·tan(π/5)), which evaluates to ¼√(5(5+2√5))·s² ≈ 1.720477·s².

Formulas

Area

A = 5s² / (4·tan(π/5)) = ¼√(5(5+2√5))·s² ≈ 1.720477·s²

Apothem

a = s / (2·tan(π/5))

Worked example

With the default values below, Pentagon Area Calculator returns Area of one pentagon of 61.9372. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side lengthminimum 0
6
Number of shapesminimum 1
1

Results

Area of one pentagon
61.9372
Perimeter
30.0000
Apothem
4.1291
Total area of all shapes
61.9372

Step by step

  1. 1Values used
  2. 2Area
  3. 3Apothem
  4. 4Area of one pentagon= 61.9372
  5. 5Perimeter= 30.0000
  6. 6Apothem= 4.1291
  7. 7Total area of all shapes= 61.9372

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 pentagon?

(5 − 2) × 180° / 5 = 108°.

Does the formula need a regular pentagon?

Yes. For an irregular pentagon use the shoelace formula on its vertex coordinates instead.

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