Golden Ratio Calculator (φ = 1.618…)
Enter a length and say which part it is.
Your numbers
Your results
Longer part (a)
Longer part (a)
—
Shorter part (b)
—
Whole (a + b)
—
φ
—
Golden Ratio Calculator (φ = 1.618…) by TheCalcTools
How the Golden Ratio Calculator (φ = 1.618…) 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 ≈ 1.618034.
φ satisfies φ² = φ + 1. It appears in regular pentagons and the Fibonacci sequence (ratios of consecutive Fibonacci numbers approach φ); claims about its use in art and nature are often exaggerated.
The formula
φ = (1 + √5) ÷ 2; a = whole ÷ φ; b = a ÷ φ
Worked example
Using the default values shown in the calculator:
| Known length | 100 |
|---|---|
| This length is | The whole (a + b) |
- 100 split in the golden ratio: 61.8034 and 38.1966.
Result:
| Longer part (a) | 61.8034 |
|---|---|
| Shorter part (b) | 38.1966 |
| Whole (a + b) | 100.0000 |
| φ | 1.6180 |
Frequently asked questions
What is the golden ratio of 100?
Split 100 into 61.8034 and 38.1966.
Sources and further reading
Related calculators
More in Math · All calculators
This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.