Golden Ratio Calculator
Split a length into two parts in the golden ratio, from the longer part, the shorter part or the whole.
Longer part
10
- Shorter part (b)
- 6.18034
- Whole (a + b)
- 16.18034
- Check of the ratio
- a ÷ b = 1.618033989, and φ = 1.618033989
The longer part is 10 and the shorter part is 6.1803.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| The golden ratio | φ = (1 + √5) ÷ 2 | 1.6180339887 |
| The other part | 10 ÷ φ | 6.18034 |
How it works
Choose which part you know, then type its length.
Worked example
A whole length of 100:
- Longer part: 100 ÷ 1.618034 = 61.8034
- Shorter part: 100 − 61.8034 = 38.1966
- Check: 61.8034 ÷ 38.1966 = 1.618034
Sources
Frequently asked questions
What is the golden ratio?
The golden ratio, φ (phi), is about 1.6180339887. Two parts are in the golden ratio when the whole is to the longer part as the longer part is to the shorter part. It equals (1 + √5) ÷ 2.
How do you find the shorter part from the longer part?
Divide the longer part by φ. If the longer part is 10, the shorter part is 10 ÷ 1.618 = 6.18.
How do you find the longer part from the shorter part?
Multiply the shorter part by φ. If the shorter part is 10, the longer part is 10 × 1.618 = 16.18.
How do you split a whole into golden parts?
Divide the whole by φ to get the longer part, then subtract it from the whole. A length of 100 splits into 61.8 and 38.2.
Where is the golden ratio used?
It appears in geometry, in the pentagon and the Fibonacci sequence, and designers and artists sometimes use it for proportions. Whether it makes a design look better is a matter of taste.