Heptagon Calculator — Area, Perimeter, Apothem & Diagonals
Find every geometric property of a regular (equilateral, equiangular) heptagon from a single side length — area, perimeter, apothem, circumradius, interior and exterior angles, and diagonal lengths.
Area of the regular heptagon = 7s² / (4 tan(π/7))
- 1
s²
1 × 1 = 1 - 2
4 × tan(π/7)
1.9263Constant divisor for a regular heptagon area formula. - 3
Area
7 × 1 ÷ 1.9263 = 3.6339
How does this calculator work?
A regular heptagon with side s has: area = 7s²/(4tan(π/7)) ≈ 3.634s², perimeter = 7s, apothem = s/(2tan(π/7)) ≈ 1.038s, circumradius = s/(2sin(π/7)) ≈ 1.152s, interior angle ≈ 128.57°, and 14 diagonals of two distinct lengths.
Formula
How this is calculated
A regular heptagon is a seven-sided polygon with all sides equal and all interior angles equal. The interior angle at each vertex is (7 − 2) × 180° / 7 = 900/7 ≈ 128.571°, and the exterior angle is 360° / 7 ≈ 51.429°. Because the number 7 does not divide 360° evenly, a regular heptagon cannot be constructed with compass and straightedge alone — it requires approximate methods or trigonometry.
All properties derive from the side length s and the central angle π/7 radians. The apothem (inradius a) is the perpendicular distance from the centre to the midpoint of a side: a = s / (2 tan(π/7)). The circumradius R is the distance from the centre to a vertex: R = s / (2 sin(π/7)). The area equals 7/2 × a × s (seven triangles each with base s and height a) which simplifies to 7s² / (4 tan(π/7)). There are two distinct diagonal lengths: the short diagonal spanning one skip vertex (d₁ = 2R sin(2π/7)) and the long diagonal spanning two skip vertices (d₂ = 2R sin(3π/7)). The total number of diagonals is 7 × (7 − 3) / 2 = 14.
Frequently asked questions
A heptagon is a polygon with seven sides. A regular heptagon has all sides equal and all interior angles equal (≈128.57° each). It appears in coins such as the British 50p and 20p pieces, which use a Reuleaux heptagon shape.
By Gauss's theorem, a regular n-gon is constructible when n is a product of a power of 2 and distinct Fermat primes (3, 5, 17, 257, 65537). Since 7 is not in that set, exact construction is impossible without trigonometric tools.
A heptagon has 7 × (7 − 3) / 2 = 14 diagonals. A regular heptagon has two distinct diagonal lengths: a short diagonal (skipping one vertex) and a long diagonal (skipping two vertices).
Also known as
TG we-Calculate Editorial Team. (2026). Heptagon Calculator — Area, Perimeter, Apothem & Diagonals [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/heptagon-calculator
TG we-Calculate Editorial Team. "Heptagon Calculator — Area, Perimeter, Apothem & Diagonals." TG we-Calculate. 2026. https://we-calculate.com/calculator/heptagon-calculator.
TG we-Calculate Editorial Team, "Heptagon Calculator — Area, Perimeter, Apothem & Diagonals," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/heptagon-calculator
@misc{wecalculate_heptagon_calculator, title = {Heptagon Calculator — Area, Perimeter, Apothem & Diagonals}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/heptagon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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