Golden Ratio Calculator & Visualizer
Enter any length to get its golden ratio pair: the value multiplied and divided by φ (1.618). View it as a golden rectangle, spiral or line split. How it works
Use the Golden Ratio Calculator & Visualizer
About the Golden Ratio Calculator & Visualizer
The golden ratio is φ = 1.618034. Multiply a length by 1.618 to get its longer golden partner; divide by 1.618 (the same as multiplying by 0.618) to get the shorter one. Enter a length up to 10,000 and this golden ratio calculator shows both, to two decimals, or tell it the length is the whole, the longer part or the shorter part of a golden split and it gives the other two: a whole of 100 splits into 61.80 and 38.20. Check a ratio takes two lengths you already have and says how far their ratio is from φ.
Golden ratio pairs for common lengths
| Length | × φ (longer partner) | ÷ φ (shorter partner, 61.8%) | Remainder (38.2%) |
|---|---|---|---|
| 16 | 25.89 | 9.89 | 6.11 |
| 100 | 161.80 | 61.80 | 38.20 |
| 300 | 485.41 | 185.41 | 114.59 |
| 500 | 809.02 | 309.02 | 190.98 |
| 618 | 999.95 | 381.95 | 236.05 |
| 960 | 1553.31 | 593.31 | 366.69 |
| 1000 | 1618.03 | 618.03 | 381.97 |
| 1200 | 1941.64 | 741.64 | 458.36 |
| 1440 | 2329.97 | 889.97 | 550.03 |
| 1920 | 3106.63 | 1186.63 | 733.37 |
Any unit works: px, mm, inches. The × φ and ÷ φ columns are the two results the calculator shows. The last column is the length minus the ÷ φ value, so the last two columns are the two parts of a golden split.
Ratios of consecutive Fibonacci numbers
| Pair | Ratio |
|---|---|
| 3 ÷ 2 | 1.500000 |
| 5 ÷ 3 | 1.666667 |
| 8 ÷ 5 | 1.600000 |
| 13 ÷ 8 | 1.625000 |
| 21 ÷ 13 | 1.615385 |
| 34 ÷ 21 | 1.619048 |
| 55 ÷ 34 | 1.617647 |
| 89 ÷ 55 | 1.618182 |
| 144 ÷ 89 | 1.617978 |
φ = 1.618034. Each ratio lands on the other side of φ from the one before, and closer to it.
Checking two lengths against φ
| Lengths | Ratio (larger ÷ smaller) | Difference from φ | Verdict |
|---|---|---|---|
| 1000 and 618 | 1.6181 | +0.0001 (0.01%) | Golden |
| 21 and 13 | 1.6154 | -0.0026 (0.16%) | Golden |
| 5 and 3 | 1.6667 | +0.0486 (3.01%) | Close |
| 16 and 10 | 1.6000 | -0.0180 (1.11%) | Close |
| 3 and 2 | 1.5000 | -0.1180 (7.29%) | Not golden |
| 1920 and 1080 | 1.7778 | +0.1597 (9.87%) | Not golden |
| 297 and 210 | 1.4143 | -0.2037 (12.59%) | Not golden |
The bands are this calculator's own convention, not a standard: within 0.5% of φ is golden, within 5% is close. 1920 × 1080 is a 16:9 screen and 297 × 210 mm is A4 paper.
Frequently asked questions
- What is the golden ratio formula?
- Two lengths a and b, with a the longer, are in the golden ratio when (a + b) ÷ a = a ÷ b. The only positive solution is φ = (1 + √5) ÷ 2 = 1.6180339887...
- How do I check if two lengths are in the golden ratio?
- Divide the larger by the smaller and compare the result with 1.618. Type both under Check a ratio and the calculator does it: 21 and 13 give 1.6154, 0.16% below φ. It calls a ratio golden within 0.5% of φ and close within 5%; those bands are its own convention, since no standard sets a tolerance.
- How do I split a line or a layout width in the golden ratio?
- Give the larger part 61.8% and the smaller part 38.2%. A 1200 px layout splits into 741.64 px and 458.36 px; a 960 px one into 593.31 px and 366.69 px. Set My number is the to Whole and the calculator lists both parts.
- I know one part of a golden split. How do I find the others?
- Set My number is the to Longer part or Shorter part and type it. The longer part is the shorter part × φ, and the whole is the longer part × φ. A shorter part of 100 gives a longer part of 161.80 and a whole of 261.80; a longer part of 100 gives a shorter part of 61.80 and a whole of 161.80.
- What are the dimensions of a golden rectangle?
- The long side is 1.618 times the short side. The Rectangle view takes the value you enter as the short side: 1000 draws a 1618.03 × 1000 rectangle. If you know the long side, read the smaller result instead: a rectangle 1920 wide is 1186.63 tall.
- How do I make a golden ratio type scale?
- Enter your body size and feed each larger result back in: 16 px × 1.618 = 25.89 px, and 25.89 px × 1.618 = 41.89 px. That gives a three-step scale of 16, 25.89 and 41.89 px. The tool works one step at a time and does not list a whole scale.
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