What the golden ratio is
The golden ratio, written φ (phi), is (1 + √5) ÷ 2, about 1.618. Two parts are in the golden ratio when the whole divided by the longer part equals the longer part divided by the shorter part. Designers, photographers and architects use it because the proportion feels balanced.
How to use it
- Fill in one box: the longer part, the shorter part or the total.
- Press Find golden ratio.
- See all three lengths with the working.
The method
- Longer = shorter × 1.618
- Shorter = longer ÷ 1.618
- Longer = total ÷ 1.618 (about 61.8% of the total)
Total 100 ⇒ longer = 1001.618 ≈ 61.8, shorter = 100 − 61.8 = 38.2
Examples you can try
| You enter | Longer | Shorter | Total |
|---|---|---|---|
| Total 100 | 61.8 | 38.2 | 100 |
| Longer 50 | 50 | 30.9 | 80.9 |
| Shorter 10 | 16.18 | 10 | 26.18 |
Where people use it
- Layout and web design: choose a main column and a sidebar, such as 62% and 38%.
- Photography: place subjects along golden lines.
- Woodwork and framing: cut a board or mat to a pleasing proportion.
Tips
- The golden ratio is a guide, not a rule. Use it when it looks right to you.
- Read the golden ratio guide for its history and common myths.
Want to learn the method?
The golden ratio explainedRead our short guide with worked examples you can follow on paper.
Frequently asked questions
What is the golden ratio?
A proportion of about 1.618 to 1, where the whole is to the longer part as the longer part is to the shorter part.
How do I split a length in the golden ratio?
Divide the length by 1.618 to get the longer piece, then subtract it from the length for the shorter piece.
Is the golden ratio exactly 1.618?
It is an irrational number, about 1.6180339887. The calculator uses the exact value.
What is the golden ratio as a percent?
About 61.8% and 38.2%.
Is it related to Fibonacci numbers?
Yes. Ratios of consecutive Fibonacci numbers get closer to 1.618.