Case 1
- Total length to divide
- 100
61.803399
Open with these valuesGolden Ratio Calculator
61.803399
Result: 61.803399φ = (1 + √5) ÷ 2 = 1.618033988749895, and that is a definition, not a measurement. Divide your total by φ and you have the longer part, the answer here. Subtract it from the total for the shorter one: 100 splits into 61.803399 and 38.196601. Any unit works, because φ is a pure proportion.
The numbers at a glance
| Total length to divide | Result |
|---|---|
| 25.000000 | 15.450850 |
| 50.000000 | 30.901699 |
| 75.000000 | 46.352549 |
| 100.000000Your value | 61.803399 |
| 125.000000 | 77.254249 |
| 150.000000 | 92.705098 |
| 175.000000 | 108.155948 |
| 200.000000 | 123.606798 |
Worked examples
Case 2
- Total length to divide
- 10
6.180340
Open with these valuesCase 3
- Total length to divide
- 1
0.618034
Open with these valuesHow it's calculated
longer = total ÷ φ, with φ = (1 + √5) ÷ 2
- StepEnter the whole length you want to split, in any unit you like.
- StepDivide it by φ = 1.618033988749895 to get the longer part.
- StepSubtract the longer part from the total to get the shorter one.
- ResultBoth parts come back in the unit you entered.
Reference table
| Total length | Shorter part | Longer part |
|---|---|---|
| 1 | 0.381966 | 0.618034 |
| 2 | 0.763932 | 1.236068 |
| 10 | 3.819660 | 6.180340 |
| 100 | 38.196601 | 61.803399 |
| 1000 | 381.966011 | 618.033989 |
Questions
What is the golden ratio?
It is the proportion φ = (1 + √5) ÷ 2 ≈ 1.618, written with the Greek letter phi. Split a line so that the whole divided by the longer part equals the longer part divided by the shorter part, and both ratios come out as φ.
How do I divide a length in the golden ratio?
Divide the total by φ for the longer part, then subtract that from the total for the shorter one. For a total of 100 the longer part is 61.803399 and the shorter 38.196601, and 61.8 ÷ 38.2 is φ again.
Why is the golden ratio considered special?
Because the longer part relates to the shorter exactly as the whole relates to the longer — a self-similar proportion. It is also the limit that consecutive Fibonacci numbers approach, which is why it turns up in shells, sunflowers and plant branching.
How is it different from the rule of thirds?
The rule of thirds cuts a frame into three equal parts; the golden ratio cuts it at roughly 62 percent and 38 percent. The golden cut sits a little closer to the centre than the thirds line.
Which units can I use?
Any of them, because the golden ratio is a pure proportion — pixels, centimetres, inches or points all behave alike. Enter the total in the unit you work in and both parts come back in that same unit.
Sources and last check
Information, not professional advice.