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
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
Formula (LaTeX) + variables + units
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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: \( \theta = \frac{(7-2)\times 180^\circ}{7} = \frac{900^\circ}{7} \approx 128.571^\circ \)
- No variables provided in audit spec.
- 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/
Last code update: 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.