Heptagon Area Calculator — From Side, Circumradius or Apothem
Find the area of a regular heptagon from whichever dimension you know: side length, circumradius (centre-to-vertex distance), or apothem (centre-to-midpoint distance). The calculator also returns all derived measurements.
Calculate area from
Area of the regular heptagon
- 1
s²
1 × 1 = 1 - 2
4 × tan(π/7)
1.926298Constant for a regular heptagon: 4 × tan(π/7). - 3
Area
7 × 1 ÷ 1.926298 = 3.633912
How does this calculator work?
The area of a regular heptagon equals 7s²/(4 tan(π/7)) ≈ 3.6339s² from side s, (7R²/2) sin(2π/7) ≈ 3.3710R² from circumradius R, or 7a² tan(π/7) ≈ 3.3710a² from apothem a. All three formulas are equivalent; choose whichever dimension you know.
Formula
How this is calculated
A regular heptagon (7 equal sides, 7 equal angles) can be described by three related radii: the side length s, the circumradius R (distance from the centre to each vertex), and the apothem a (perpendicular distance from the centre to the midpoint of each side). They are related by a = R cos(π/7) and s = 2R sin(π/7) = 2a tan(π/7).
The area can be found from any of the three. Given side s: the heptagon is divided into 7 congruent isosceles triangles, each with base s and height a = s/(2 tan(π/7)), giving area = 7 × (½ × s × a) = 7s²/(4 tan(π/7)). Given circumradius R: each triangle has two sides equal to R and a vertex angle of 2π/7, giving area = 7 × (½ × R² × sin(2π/7)) = (7R²/2) sin(2π/7). Given apothem a: substituting s = 2a tan(π/7) into the first formula gives area = 7a² tan(π/7).
All three formulas are mathematically equivalent — the calculator converts whichever input you provide into the others and computes the area using the most direct formula for that input type.
Frequently asked questions
The circumradius R is the radius of the circle that passes through all 7 vertices (the circumscribed circle). The apothem a is the radius of the circle that is tangent to all 7 sides (the inscribed circle). For a regular heptagon, a = R cos(π/7) ≈ 0.9009 R.
With s = 1: area = 7/(4 tan(π/7)) ≈ 3.6339 square units. The apothem is ≈ 1.0383 and the circumradius is ≈ 1.1524.
The heptagon area calculator focuses on computing area from three different starting dimensions (side, circumradius, or apothem), whereas the heptagon calculator takes only the side length but returns all geometric properties including diagonal lengths and angles.
Also known as
TG we-Calculate Editorial Team. (2026). Heptagon Area Calculator — From Side, Circumradius or Apothem [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/heptagon-area-calculator
TG we-Calculate Editorial Team. "Heptagon Area Calculator — From Side, Circumradius or Apothem." TG we-Calculate. 2026. https://we-calculate.com/calculator/heptagon-area-calculator.
TG we-Calculate Editorial Team, "Heptagon Area Calculator — From Side, Circumradius or Apothem," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/heptagon-area-calculator
@misc{wecalculate_heptagon_area_calculator, title = {Heptagon Area Calculator — From Side, Circumradius or Apothem}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/heptagon-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?