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°

Copied to clipboard

Summary

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

How it works

Enter the side length of a regular pentagon in the input field.
Select a unit (mm, cm, m, in, ft) from the dropdown.
Click "Calculate Area" to apply the formula A = (s² × √(25 + 10√5)) / 4.
The result is displayed with up to 6 significant figures.
The step-by-step working breaks down each arithmetic operation.
Use the Copy button to copy the result to your clipboard.

Use cases

Geometry homework and exam problems involving regular pentagons.
Architecture and design work with pentagonal floor plans or tiles.
Engineering drawings that include pentagonal cross-sections.
Verifying manual pentagon area calculations quickly.
Teaching the regular polygon area formula in the classroom.
Calculating material or land area for five-sided lots.
Game development requiring polygon surface-area computation.
3D modeling where a pentagonal base area is needed.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu