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

The formula is A = (7/4) × s² × cot(π/7), where s is the side length and cot(π/7) = cos(π/7) / sin(π/7). The numeric multiplier is approximately 3.6339, so A ≈ 3.6339 × s².

What is a regular heptagon?

A regular heptagon is a seven-sided polygon with all sides equal in length and all interior angles equal. Each interior angle measures exactly 900°/7 ≈ 128.57°.

Does this calculator work for irregular heptagons?

No. This calculator is for regular heptagons only — seven equal sides and seven equal angles. For irregular heptagons, divide the shape into triangles and sum their individual areas.

What units does the result use?

The area is expressed in square units matching your chosen unit. For example, entering 5 cm gives an area in cm².

Why does the formula use cot(π/7)?

The general formula for any regular n-gon is A = (n/4) × s² × cot(π/n). For a heptagon n = 7, so cot(π/7) appears because it relates the side length to the apothem (the perpendicular distance from the center to a side), which drives the enclosed area.

How do I find the side length if I know the area?

Rearrange the formula: s = √(A / 3.6339). Divide the area by approximately 3.6339 and take the square root.

Area of a Heptagon Calculator

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

Enter the side length of a regular heptagon to instantly calculate its area using the exact formula A = (7/4) × s² × cot(π/7) with step-by-step working.

Heptagon Dimensions

Side length (s)

Unit

Formula

A = (7/4) × s² × cot(π/7)

≈ 3.6339 × s²

Area

—

Enter a value and click Calculate

Heptagon diagram

All sides equal (s), all interior angles ≈ 128.57°, apothem (a) shown

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Summary

Enter the side length of a regular heptagon to instantly calculate its area using the exact formula A = (7/4) × s² × cot(π/7) with step-by-step working.

How it works

Enter the side length of the regular heptagon in the input field.
Choose your preferred unit from the dropdown (mm, cm, m, in, ft).
Click "Calculate Area" to apply the formula A = (7/4) × s² × cot(π/7).
The result is displayed with up to 6 significant figures.
A step-by-step breakdown shows every arithmetic operation used.

Use cases

Geometry homework and exam problems involving regular heptagons.
Architecture and design using seven-sided floor or tile plans.
Engineering drawings with heptagonal cross-sections.
Game development requiring polygon area computation.
Teaching regular polygon area formulas in the classroom.
Verifying manual heptagon area calculations quickly.
Land surveying or landscaping with heptagonal plots.
Creating heptagonal decorative or structural elements.

Frequently Asked Questions

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