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

The area formula is A = (9/4) × s² × cot(π/9), where s is the length of one side and cot is the cotangent function. The constant (9/4)cot(π/9) is approximately 6.18182. This formula applies only to regular nonagons — those with all sides equal and all interior angles equal to 140°.

Does this work for irregular nonagons?

No. The formula A = (9/4)s²cot(π/9) is valid only for regular nonagons. An irregular nonagon (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 nonagon?

The perimeter is simply 9 × s, since a regular nonagon has nine equal sides. This calculator shows the perimeter alongside the area for convenience.

What are the interior angles of a regular nonagon?

Each interior angle of a regular nonagon measures 140°. The sum of all interior angles is (9 − 2) × 180° = 1260°.

Area of a Nonagon Calculator

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

Enter the side length of a regular nonagon to instantly calculate its area using the formula A = (9/4) × s² × cot(π/9).

Input

Side Length (s)

Formula

A = (9/4) × s² × cot(π/9)

where s = side length

Constant ≈ 6.181824

Result

Enter a side length and click Calculate

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Summary

Enter the side length of a regular nonagon to instantly calculate its area using the formula A = (9/4) × s² × cot(π/9).

How it works

Enter the side length of the regular nonagon in the input field.
Choose your preferred unit (millimeters, centimeters, meters, inches, or feet).
The area is calculated instantly using the formula A = (9/4) × s² × cot(π/9).
View the step-by-step breakdown showing intermediate values.
Copy the result or reset the form to start over.

Use cases

Calculating floor area for nonagonal room layouts or tile patterns.
Estimating material for nine-sided garden beds or patio sections.
Architecture and engineering projects with nine-sided structures.
Homework and exam preparation for geometry or trigonometry courses.
Verifying manual calculations for DIY or construction projects.
Computing surface areas for nonagonal signs, art installations, or decorations.

Frequently Asked Questions

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