How this calculator works
Seven equal central triangles split a regular heptagon. Their half-angle is π/7, which relates a side to the apothem and circumradius. The coordinate table places the centre at (0,0), with vertex 1 on the positive x-axis and the others in counterclockwise order. Joining vertices two steps apart gives one diagonal class, while three steps apart gives the other. Each class has seven members, giving fourteen diagonals altogether. These measurements apply to a regular heptagon, not merely any seven-sided outline.
Formula
P=7a; apothem r=a/[2tan(π/7)]; circumradius R=a/[2sin(π/7)]; A=7ar/2. A chord spanning k vertex steps has length 2R sin(kπ/7). Vertex i is (R cos(2πi/7), R sin(2πi/7)) for i=0,...,6.
Worked example
For side 2 m, the perimeter is 14 m and area is about 14.53564978 m². There are seven short diagonals and seven long diagonals. Doubling the side to 4 m doubles every chord length and quadruples the area to about 58.14259910 m².
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Frequently asked questions
Why are there two diagonal lengths?
A chord can skip one vertex or two vertices before reaching its endpoint. Longer step counts trace the same chords in the reverse direction.
Where is the first vertex in the coordinate table?
It lies at (R,0). Rotate every point by the same angle if your drawing needs a different orientation.
Can I size the heptagon from its apothem?
Yes. Choose apothem and enter the perpendicular centre-to-side distance. This input is useful when the polygon must fit around an inscribed circle.