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

The area formula is A = (5/2) × s² × cot(π/10), where s is the length of one side and cot is the cotangent function. This simplifies from the general polygon formula A = (n/4) × s² × cot(π/n) for n = 10. The constant (5/2)cot(π/10) is approximately 7.6942. This formula applies only to regular decagons — those with all sides equal and all interior angles equal to 144°.

Does this work for irregular decagons?

No. The formula A = (5/2)s²cot(π/10) is valid only for regular decagons. An irregular decagon (with unequal sides or angles) requires a different approach, such as dividing it into triangles or using the shoelace formula with vertex coordinates.

What units does the calculator use?

You can enter the side length in millimeters, centimeters, meters, inches, or feet. The result is displayed in the corresponding square unit (e.g., cm² if you enter centimeters).

How accurate is the result?

The calculation uses JavaScript's full floating-point precision (IEEE 754 double). Results are displayed rounded to 6 significant figures, which is sufficient for virtually all practical applications.

What is the perimeter of a regular decagon?

The perimeter is simply 10 × s, since a regular decagon has ten equal sides. This calculator shows the perimeter alongside the area for convenience.

What are the interior angles of a regular decagon?

Each interior angle of a regular decagon measures 144°. The sum of all interior angles is (10 − 2) × 180° = 1440°.

Area of a Decagon Calculator

Enter the side length of a regular decagon to instantly calculate its area using the formula A = (5/2) × s² × cot(π/10).

Input

Side Length (s)

Formula

A = (5/2) × s² × cot(π/10)

where s = side length

Constant ≈ 7.694209

Shape Preview

Result

Enter a side length and click Calculate

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Summary

This calculator computes the area of a regular decagon — a ten-sided polygon with all sides equal and all interior angles equal to 144° — using the standard geometric formula A = (5/2) × s² × cot(π/10), where s is the side length. The constant factor (5/2)cot(π/10) is approximately 7.6942. Results are shown in square units matching your input along with a full step-by-step breakdown and an SVG shape preview.

How it works

Enter the side length of the regular decagon in the input field.
Choose your preferred unit (millimeters, centimeters, meters, inches, or feet).
The area is calculated instantly using the formula A = (5/2) × s² × cot(π/10).
View the SVG preview that scales with the side length you entered.
Check the step-by-step breakdown showing each intermediate calculation.
Copy the result or reset the form to start over.

Use cases

Calculating floor area for decagonal room layouts or tile patterns.
Estimating material for ten-sided garden beds or patio sections.
Architecture and engineering projects involving ten-sided structures.
Homework and exam preparation for geometry or trigonometry courses.
Verifying manual calculations for DIY or construction projects.
Computing surface areas for decagonal signs, art installations, or decorations.
Urban planning for decagonal plazas or roundabouts.
Woodworking and craft projects requiring precise polygon measurements.

Frequently Asked Questions

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