Regular Polygon Diagonals Calculator
This calculator computes the regular polygon diagonals: exact formula d = 2R·sin(kπ/n), worked example octagon R = 4 → 20 diagonals, shortest 5.66.
- Free, instant, any units.
Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.
How the regular polygon diagonals Calculator Works
The calculator applies the exact formula count = n(n−3)/2, length dₖ = 2R·sin(kπ/n). Worked example: octagon R = 4 cm → 20 diagonals, shortest 5.66 cm. Keep every input in one unit system and the result follows in length units (m, ft, cm); full precision is kept until the final rounding.
- 1
Enter the measurements
Type the values required by the formula for regular polygon diagonals.
- 2
Check the units
One unit system throughout — cm, m, ft or in.
- 3
Read the result
The calculator substitutes, evaluates and rounds only at the end.
Use Cases
Frame bracing and layout diagonals
Verifying member lengths in drawings
Geometry coursework on polygons
Tips
- 1
Diagonals split polygons into triangles
- 2
Count diagonals with n(n−3)/2 before measuring
- 3
Longer diagonal means flatter shape — sanity check
Common Mistakes
Counting sides as diagonals
Using the wrong vertex skip k in dₖ = 2R·sin(kπ/n)
Assuming diagonals equal in non-square shapes
FAQs
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