Star Shape Calculator

Your details

The number of outward-pointing tips on the star. A 5-pointed star is a pentagram, 6-pointed is a hexagram.
Distance from the centre of the star to the tip of each point. Sometimes called the circumradius.
cm
Distance from the centre to each inner valley vertex, where the edges of the star meet between two tips. Must be less than the outer radius.
cm
AreaSharp star
117.5571cm²

Total enclosed area of the star polygon

Perimeter71.6091cm
Edge segment length7.1609cm
Spike height6.7639cm
Tip angle38.33deg
Inner valley angle110.33deg
r / R ratio0.4
Area117.5571
Perimeter71.6091
Spike height6.7639
Edge length7.1609

5-pointed star: area 117.56 cm²

  • Your pentagram has an area of 117.56 cm² and a perimeter of 71.61 cm.
  • The tip angle is 38.3 deg. A classic five-pointed star has a tip angle of 36 deg.
  • With an r/R ratio of 0.400, the star has moderate spikes.

Next stepTo check your star fits a given bounding circle, confirm that R equals the outer radius you measured. To scale the star, multiply both R and r by the same factor - the angles stay constant.

 = Powered by OnlyCalculators