Regular Pentagon Area Calculator

Calculator Inputs

Input Method

Measurement Unit

Decimal Places

Side Length

Perimeter

Apothem

Circumradius

Diagonal

Large screens show three columns. Smaller screens use two. Mobile stacks fields into one column.

Area Growth Plot

This graph shows how pentagon area changes with side length.

Formula Used

From side length

A = (1/4) × √(5(5 + 2√5)) × s²

From perimeter

A = [√(5(5 + 2√5)) / 100] × P²

From apothem

A = 5 × a² × tan(36°)

From circumradius

A = (5/2) × R² × sin(72°)

Helpful geometry relationships

P = 5s, a = s / [2tan(36°)], R = s / [2sin(36°)], d = φs

How to Use This Calculator

Select the input method that matches your available measurement.
Enter one positive value in the active field.
Choose your unit and preferred decimal precision.
Press Calculate Area to show the result above the form.
Review the derived side, perimeter, radius, diagonal, and angles.
Use the export buttons to save the result as CSV or PDF.

Example Data Table

Side	Perimeter	Apothem	Circumradius	Diagonal	Area
3.0000	15.0000	2.0646	2.5520	4.8541	15.4843
5.0000	25.0000	3.4410	4.2533	8.0902	43.0119
8.0000	40.0000	5.5055	6.8052	12.9443	110.1106
12.0000	60.0000	8.2583	10.2078	19.4164	247.7487

These examples use generic units. Square results follow the same unit system.

Frequently Asked Questions

1. What is a regular pentagon?

A regular pentagon has five equal sides and five equal interior angles. Because all sides match, one measurement can generate many other properties accurately.

2. Which input method is best?

Use the method that matches your known value. Side length is common. Apothem and circumradius are useful in geometry and drafting problems.

3. Can I calculate area from perimeter only?

Yes. For a regular pentagon, perimeter uniquely determines side length. Once side length is known, the area follows directly from the standard formula.

4. What does the apothem mean?

The apothem is the distance from the center to the midpoint of a side. It helps connect area, side length, and perimeter efficiently.

5. Why is the diagonal longer than the side?

A pentagon diagonal connects nonadjacent vertices. In a regular pentagon, diagonal length equals the golden ratio multiplied by the side length.

6. Are the angle values always fixed?

Yes. Every regular pentagon has interior angles of 108 degrees and exterior angles of 72 degrees, regardless of its size.

7. Do the unit choices affect the answer?

The unit choice changes labels only. Enter all values in one consistent unit system. The area output becomes that unit squared.

8. What are the exports useful for?

CSV files help with spreadsheets and logs. PDF files are useful for sharing, printing, class notes, reports, and design documentation.