What is the formula for the area of a regular pentagon?

The standard formula is A = (s² × √(25 + 10√5)) / 4, where s is the side length. This simplifies to approximately A ≈ 1.720477 × s².

Does this calculator work for irregular pentagons?

No. This calculator is for regular pentagons only — five equal sides and five equal angles of 108°. For irregular pentagons, divide the shape into triangles and sum their areas.

What units does the result use?

The area is always expressed in square units of whatever unit you choose. For example, entering 5 cm gives an area in cm².

How do I find the side length from the area?

Rearrange the formula: s = √(4A / √(25 + 10√5)) = √(A / 1.720477). Take the square root of the area divided by approximately 1.720477.

What is a regular pentagon?

A regular pentagon is a five-sided polygon where all sides are equal in length and all interior angles are equal (each 108°). The US Pentagon building and the home plate in baseball are well-known examples.

Why is the formula so complex?

The constant √(25 + 10√5) comes from trigonometry — specifically from the sine of 72° multiplied by the apothem relationship in a regular pentagon. It evaluates to approximately 6.8819, giving the factor ≈ 1.720477 when divided by 4.

Area of a Pentagon Calculator

Name: Area of a Pentagon Calculator
Availability: InStock
Author: Nham Vu

Enter the side length of a regular pentagon to instantly calculate its area with the full formula and step-by-step working.

Pentagon Side Length

Side length (s)

Unit

Formula

A = (s² × √(25 + 10√5)) / 4

≈ 1.720477 × s²

Area

—

Enter a side length and click Calculate

Pentagon diagram

All sides equal, all interior angles 108°

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Summary