Decagon Calculator - Area, Perimeter, Diagonals and Radii

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Select which measurement you already know. Enter its value below.
Enter the known measurement. All other properties will be calculated from it.
cm
Side length (a)
5

Length of one of the 10 equal sides

Perimeter50
Area192.3552
Circumcircle radius (R)8.0902
Inradius / apothem (r)7.6942
Diagonal d2 (skip 1 vertex)9.5106
Diagonal d3 (skip 2 vertices)13.0902
Diagonal d4 (skip 3 vertices)15.3884
Longest diagonal (d5)16.1803

A regular decagon with side 5.0000 has area 192.3552 and perimeter 50.0000.

  • The circumcircle (through all 10 vertices) has radius 8.0902, roughly 1.618 times the side length.
  • The incircle (tangent to all 10 sides) has radius 7.6942, approximately 1.539 times the side length.
  • The longest diagonal spans 16.1803 and equals exactly 2R - it passes through the centre.
  • A decagon has 35 diagonals of 4 distinct lengths. The ratio of the longest diagonal to the side is 1/sin(18 degrees), ≈ 3.236, related to the golden ratio.

Next stepTo find the number of diagonals in any n-gon use n*(n-3)/2. For n=10: 10*7/2 = 35 diagonals.

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