Golden Ratio Calculator
Divide a length by the golden ratio phi=(1+sqrt5)/2 about 1.618. Enter the whole, the longer part, or the shorter part to get the others and a golden rectangle diagram.
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Input
Enter a known length and choose which part of the golden section it is to calculate the rest.
Part you entered
Whole
Result
Golden ratio phi
1.618034
Whole
100
Longer part
61.803399
Shorter part
38.196601
Whole to longer part and longer part to shorter part are both phi to 1.
How it works
- The golden ratio is phi=(1+sqrt5)/2 about 1.618.
- In a golden section, whole to longer part and longer part to shorter part are both phi to 1.
- If you enter the whole, the longer part is the whole divided by phi and the shorter part is the whole minus the longer part.
- If you enter the longer part, the shorter part is the longer part divided by phi and the whole is their sum.
- If you enter the shorter part, the longer part is the shorter part times phi and the whole is their sum.
Frequently asked questions
- What is the value of the golden ratio phi?
- The golden ratio is phi=(1+sqrt5)/2, about 1.618. In a golden division, whole-to-longer and longer-to-shorter are both in the ratio phi to 1.
- Which value should I enter: the whole, the longer, or the shorter part?
- Enter any one and the others follow. From the whole, the longer part is whole ÷ phi and the shorter is the remainder; from the longer part, the shorter is longer ÷ phi and the whole is their sum.
- Can it work if I only know the shorter part?
- Yes. Enter the shorter part and the longer part is shorter × phi, with the whole being their sum, plus a golden rectangle diagram.
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