Golden ratio calculator

How it works

Two lengths are in the golden ratio when the whole is to the longer part as the longer part is to the shorter: (a + b) ÷ a = a ÷ b = φ.

φ is (1 + √5) ÷ 2, about 1.6180339887. It has the property φ² = φ + 1, so the total is also the shorter part times φ².

Designers use it for layout grids and type scales, though its role in nature and classical art is often overstated.

Formula

φ = (1 + √5) ÷ 2 ≈ 1.6180339887
b = a ÷ φ
a + b = a × φ
a = total ÷ φ

Worked example

If the longer part is 100, the shorter part is 100 ÷ 1.618034 = 61.8034 and the total is 161.8034. Splitting a total of 100 gives 61.8034 and 38.1966.