Golden Ratio Calculator

Your details

Segment mode splits a length into a and b. Rectangle mode finds the matching golden rectangle side. Fibonacci mode shows how consecutive Fibonacci ratios approach phi.
The length you want to work with, in any consistent unit.
How to interpret the value you entered when splitting by phi.
Precision for all displayed results.
Whole length (a + b)
100
Longer segment (a)61.8034
Shorter segment (b)38.1966
Ratio a : b1.618 : 1
Longer segment as % of whole0.62%
phi (exact to 8 dp)1.618
Golden angle137.5078 deg
Longer segment (a)61.8034
Shorter segment (b)38.1966

The longer part is 61.8034 and the shorter part is 38.1966.

  • Each adjacent pair is in golden proportion: whole / long = long / short = phi = 1.618.
  • The longer segment is about 61.8% of the whole (61.8%), and the shorter is the remaining 38.2% (38.2%).
  • The ratio a:b = 1.618034, which should equal phi = 1.618034.
  • phi is irrational, so these segments never resolve to a clean fraction; the displayed values are rounded.

Next stepApply the longer segment again as a new whole to build self-similar nested golden rectangles or a golden spiral.

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