🌀 Golden Ratio Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
Enter one measurement and choose what it represents. The calculator splits it into the longer and shorter parts so that longer divided by shorter equals phi (about 1.618).
phi = (1 + sqrt 5) / 2 = 1.6180339887. Results are rounded for display; the ratio is kept exact internally.
The golden ratio, written as the Greek letter phi, is approximately 1.618. Two lengths are in the golden ratio when the longer divided by the shorter equals the whole divided by the longer. This calculator takes one measurement, you tell it whether that number is the longer part, the shorter part, or the whole, and it splits the rest into golden proportion. It is a quick way to size design elements, layouts, type scales, and frames so they sit in the proportion many people find naturally pleasing.
What is the Golden Ratio Calculator?
The golden ratio is an exact number, not a rough rule of thumb. It equals (1 + sqrt 5) divided by 2, which works out to 1.6180339887 and so on forever. It is usually written with the Greek letter phi. A line is divided in golden proportion when the longer segment a and the shorter segment b satisfy a / b = (a + b) / a. Both of those fractions equal phi, which is what makes the proportion self-similar: the relationship between the parts is the same as the relationship between the larger part and the whole.
A neat property falls out of that definition. Because (a + b) / a = phi, the whole is always the longer part multiplied by phi. And because a / b = phi, the longer part is the shorter part multiplied by phi. So moving up the scale you multiply by 1.618 each step, and moving down you divide by 1.618. That is why a string of golden measurements (for example 1, 1.618, 2.618, 4.236) feels like a smooth progression: each term is phi times the one before, the same growth pattern you see in the Fibonacci sequence, whose ratios close in on phi.
In practice the golden ratio is used as a starting proportion for things like page layouts, logo grids, spacing scales, and photo crops. It is a guide, not a law: plenty of admired designs ignore it entirely, and the claim that it appears everywhere in nature and art is often overstated. Treat it as one useful proportion in your toolkit. Enter a width, a margin, or a total size, decide which role that number plays, and let the calculator hand you the matching golden parts to work from.
When to use it
- Splitting a page or canvas into a larger and smaller region (for example a content column and a sidebar) in golden proportion.
- Building a type scale or spacing scale where each step is 1.618 times the last for a harmonious rhythm.
- Cropping or framing a photo so the main subject sits on a golden division rather than dead centre.
- Sizing a logo, button, or card so its width and height relate by phi for a balanced look.
How to use the Golden Ratio Calculator
- Enter the one measurement you already know, such as a total width or a single segment length.
- Choose what that number represents: the longer part, the shorter part, or the whole (longer plus shorter).
- Read off the longer part, the shorter part, and the whole, all in golden proportion.
- Use the parts as your dimensions, or feed the longer part back in to step the scale up again.
Formula & method
Worked examples
You have a total width of 100 px and want to split it into golden proportion.
- The value is the whole, so total = 100.
- Longer part a = total / phi = 100 / 1.6180339887 = 61.803399
- Shorter part b = total - a = 100 - 61.803399 = 38.196601
- Check: a / b = 61.803399 / 38.196601 = 1.618034 (phi)
Result: Longer 61.803399, shorter 38.196601, which add back to 100.
You know the longer part is 50 and want the matching shorter part and whole.
- The value is the longer part, so a = 50.
- Shorter part b = a / phi = 50 / 1.6180339887 = 30.901699
- Whole = a x phi = 50 x 1.6180339887 = 80.901699 (also a + b)
- Check: a / b = 50 / 30.901699 = 1.618034 (phi)
Result: Shorter 30.901699, whole 80.901699.
You know the shorter part is 10 and want the longer part and whole.
- The value is the shorter part, so b = 10.
- Longer part a = b x phi = 10 x 1.6180339887 = 16.180340
- Whole = b x phi^2 = 10 x 2.618034 = 26.180340 (also a + b)
- Check: a / b = 16.180340 / 10 = 1.618034 (phi)
Result: Longer 16.180340, whole 26.180340.
Powers of phi: each step multiplies the one before by 1.618
| Expression | Value | Meaning |
|---|---|---|
| phi^0 | 1.000000 | Starting unit |
| phi^1 | 1.618034 | One golden step up |
| phi^2 | 2.618034 | Two steps (also phi + 1) |
| phi^3 | 4.236068 | Three steps |
| phi^4 | 6.854102 | Four steps |
| 1 / phi | 0.618034 | One golden step down (the shorter share of 1) |
Splitting a whole into golden parts (longer plus shorter)
| Whole | Longer part (a) | Shorter part (b) |
|---|---|---|
| 10 | 6.180340 | 3.819660 |
| 100 | 61.803399 | 38.196601 |
| 960 | 593.310424 | 366.689576 |
| 1000 | 618.033989 | 381.966011 |
Common mistakes to avoid
- Using 1.6 instead of 1.618. Rounding phi to 1.6 is close but not exact, and small errors compound when you step a scale several times. Use 1.618 (or more digits) for anything that has to add back up cleanly.
- Mixing up which part the longer ratio applies to. The longer part divided by the shorter equals phi, not the other way round. If your shorter part comes out bigger than the longer one, you have divided in the wrong direction.
- Forgetting the parts must sum to the whole. The longer and shorter parts always add up to the total. If you size two regions independently and they do not sum to your canvas, they are not in true golden proportion to the whole.
- Treating the golden ratio as a rule that guarantees good design. Phi is a helpful starting proportion, not a guarantee. Context, content, and balance matter more, so use it as a guide and adjust by eye.
Glossary
- Golden ratio
- The proportion in which the longer part divided by the shorter equals the whole divided by the longer, about 1.618.
- Phi
- The Greek letter naming the golden ratio, equal to (1 + sqrt 5) / 2 = 1.6180339887.
- Golden section
- A line divided so the two segments are in the golden ratio; another name for the split this tool produces.
- Longer part (a)
- The bigger of the two segments. It equals the shorter part times phi and the whole divided by phi.
- Shorter part (b)
- The smaller of the two segments. It equals the longer part divided by phi.
- Fibonacci sequence
- The series 1, 1, 2, 3, 5, 8, 13 and so on, where the ratio of each term to the previous one closes in on phi.
Frequently asked questions
What is the golden ratio?
The golden ratio is the number phi, about 1.618, where two lengths relate so the longer divided by the shorter equals the whole divided by the longer. Exactly, phi = (1 + sqrt 5) / 2 = 1.6180339887.
How do I calculate the golden ratio of a number?
Decide whether your number is the longer part, the shorter part, or the whole. To split a whole into golden parts, the longer part is the whole divided by 1.618 and the shorter part is what remains. This calculator does all three cases for you.
What is phi exactly?
Phi is (1 + the square root of 5) divided by 2. Written out that is 1.6180339887 and the digits continue forever, so it is an irrational number, much like pi.
How is the golden ratio related to Fibonacci numbers?
In the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13 and so on) each number is the sum of the two before it. As the numbers grow, the ratio of one term to the previous one gets closer and closer to phi, 1.618.
Is the golden ratio actually used in design?
Yes, designers often use it as a starting proportion for layouts, type scales, logos, and crops. It is a guide rather than a strict rule, and many good designs do not rely on it, so treat it as one useful tool.
What is 1 divided by phi?
1 divided by phi is about 0.618, which also equals phi minus 1. If you split a length of 1 in golden proportion, the longer part is 0.618 and the shorter part is 0.382, and 0.618 divided by 0.382 is again 1.618.