Golden Calculator

Any unit at all - the ratio is dimensionless, so the answers come back in whatever unit you enter.
Check mode: the quantity you want on top of the ratio.
Check mode: the quantity you want underneath.
Longer segment (a)
61.803399
Golden Ratio Calculator
Golden ratio (phi)
1.618033988750
1 / phi
0.618033988750
Shorter segment (b)
38.196601
Whole length (a + b)
100.000000
Ratio a : b
1.6180339887
Difference from phi
0.000000 %
Reading
100 cut at 61.803399 leaves 38.196601; both a/b and (a+b)/a equal phi.
Worked out from Euclid, Elements, Book VI definition 3 and proposition 30 - a straight line cut in extreme and mean ratio and 1 other source.

How this is worked out

4 steps
  1. phi = (1 + sqrt 5) / 2 = 1.61803398875, and phi^2 = phi + 1 = 2.61803398875.
  2. Longer part = total / phi = 100 / 1.61803398875 = 61.803399.
  3. Whole = 61.803399 + 38.196601 = 100.
  4. Check: (a + b) / a = 1.6180339887 and a / b = 1.6180339887 - the defining equality of Euclid VI.3.

Results are general information, not financial, tax, legal, medical or engineering advice.