What is a regular heptagon?

A regular heptagon is a 7-sided polygon where all sides and all interior angles are equal. This calculator assumes the heptagon is regular.

How do you find the area of a heptagon?

For a regular heptagon with side length s, the area is A = (7/4) × s² × cot(π/7). The calculator uses this formula under the hood.

Can I input apothem or circumradius instead of side?

Yes. If you know the apothem, circumradius, perimeter or even the area, you can input that and the tool will convert it to side length and compute the rest.

Heptagon Calculator

Free regular heptagon calculator. Enter side, perimeter, area, apothem or circumradius and get all other heptagon properties instantly. Includes formulas, steps, and FAQ.

Full original guide (expanded)

Heptagon Calculator

This tool works with a regular heptagon (7 equal sides). Enter any one measure – side, perimeter, area, apothem, or circumradius – and we’ll compute the rest.

7 sides Bidirectional Shows formulas

I have

Value

Unit

Formulas for a regular heptagon

Let \( s \) be the side length. For n = 7 sides:

Perimeter: \( P = 7s \)

Apothem (inradius): \( a = \frac{s}{2 \tan(\pi/7)} \)

Circumradius: \( R = \frac{s}{2 \sin(\pi/7)} \)

Area (from side): \( A = \frac{7}{4} s^2 \cot(\pi/7) \)

Interior angle: \( \theta = \frac{(7-2)\times 180^\circ}{7} = \frac{900^\circ}{7} \approx 128.571^\circ \)

These identities are what the calculator uses behind the scenes. If you provide a different starting value (for example apothem), we first convert it to side length using the inverse of the corresponding formula.

Example

Example: Find the area of a regular heptagon with side 5 cm.

Use \( A = \frac{7}{4} s^2 \cot(\pi/7) \)
Compute \( s^2 = 5^2 = 25 \)
Compute \( \cot(\pi/7) \) ≈ 2.0765
Then \( A = \frac{7}{4} \times 25 \times 2.0765 \approx 90.84 \text{ cm}^2 \)

The calculator will show the area rounded to your browser’s default formatting.

Heptagon Calculator – FAQ

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

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Formula (extracted text)

Perimeter: \( P = 7s \) Apothem (inradius): \( a = \frac{s}{2 \tan(\pi/7)} \) Circumradius: \( R = \frac{s}{2 \sin(\pi/7)} \) Area (from side): \( A = \frac{7}{4} s^2 \cot(\pi/7) \) Interior angle: \( \theta = \frac{(7-2)\times 180^\circ}{7} = \frac{900^\circ}{7} \approx 128.571^\circ \)

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft

Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog

0.1.0-draft — 2026-01-19: Initial draft (review required).