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