Golden Ratio Calculator
Find the shorter part and whole from the longer golden-section part.
Formula
φ = (1 + √5)/2; b = a/φ; whole = a + b.
Longer part a: 1 m · Golden ratio φ ≈ (1+sqrt(5))÷2 · Shorter part b ≈ (1 m)÷(1.618033989) · Whole segment ≈ (1 m)+(0.6180339887)
How to use
- Enter the longer part a.
- Select its length unit.
- Read the shorter part b and whole in meters.
Examples
- Longer part 1 m gives shorter part ≈ 0.618034 m.
Frequently asked questions
Which part should I enter?
Enter the longer part, not the whole segment.
What defines the golden ratio?
The whole divided by the longer part equals the longer divided by the shorter: (a+b)/a = a/b = φ.
Is phi exact as a decimal?
No. φ is irrational; its displayed decimal is approximate.
Sources
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