Golden Ratio Calculator
Enter one length to find the other parts in the golden ratio.
What this tool does
Two parts are in the golden ratio when the longer divided by the shorter equals the whole divided by the longer, about 1.6180339887. If the shorter part is 10, the longer is 16.18 and the whole is 26.18. Enter the part you know above.
Applies φ = (1 + √5) ÷ 2 to the length you give.
Shows the other part, the whole and a numerical check.
How to use it
- Choose which length you know.
- Enter its value.
- Read the other two lengths.
- Use them in your layout or drawing.
Why use this calculator
Splits any length into two parts in the golden ratio, given the longer part, the shorter part or the whole, and shows the check that a ÷ b equals φ. The golden ratio is a classic starting proportion for layouts, logos, photo crops and furniture. The arithmetic is simple but tedious by hand, particularly when working backwards from the whole.
Why we built it
We built the golden ratio calculator to split a length from whichever part you know and to show the check a ÷ b = φ. Compare screen shapes with the aspect ratio calculator and explore the numbers with the sequence calculator.
Who this tool is for
- Designers and photographers composing layouts
- Students studying Fibonacci
- Woodworkers and makers dividing a length
When to use it
- Setting page, column or logo proportions.
- Cropping a photograph.
- Dividing a canvas or a room.
- Maths and Fibonacci homework.
How it works
φ = (1 + √5) ÷ 2 ≈ 1.6180339887. If the shorter part is b, the longer part is a = b × φ and the whole is a + b = b × φ². If the longer part is a, the shorter is a ÷ φ, and if the whole is w, the longer is w ÷ φ.
Example: with a shorter part of 10, the longer is 16.1803 and the whole is 26.1803. Ratios of consecutive Fibonacci numbers (such as 89/55) approach φ.
The golden ratio is a convenient guide, not a law of beauty. Many designs that look good do not use it.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| You know the | Shorter part (b) |
| Value | 10 |
With those inputs, the calculator returns:
- Longer part (a): 16.1803
- Shorter part (b): 10
- Whole length (a + b): 26.1803
- Golden ratio φ: 1.61803399
- Check: a ÷ b: 1.61803399
What you give it, and what you get back
| Item | Details |
|---|---|
| Known length | Shorter part, longer part or whole. |
| Value | A number above zero. |
| Output | Longer part, shorter part, whole, φ and a check. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| My design still looks off | The ratio is a guide, not a guarantee. | Adjust by eye. |
| Numbers have many decimals | φ is irrational. | Round to the precision of your tool. |
| Mixed up long and short | The labels are easy to swap. | Check the "known" setting. |
Assumptions and limitations
- Single-dimension splits.
- No spiral or grid drawing.
Frequently asked questions
What is the golden ratio?
About 1.618, the ratio where the whole is to the longer part as the longer part is to the shorter.
How do I calculate the golden ratio?
Divide the longer part by the shorter; or multiply the shorter by 1.618.
What is phi?
The Greek letter φ used for the golden ratio.
How is it related to Fibonacci numbers?
The ratio of consecutive Fibonacci numbers tends to φ.
Is it used in design?
Often as a starting proportion, but not a rule.
Is my information sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.
Sources and accuracy
The tool applies the golden ratio constant phi = (1 + sqrt(5)) divided by 2, and the standard definition that the whole is to the larger part as the larger part is to the smaller. These values follow from the mathematics of the golden section.
Figures last checked against the source on . Standards and rates can change — if you are relying on this for something that matters, confirm against the source above. Think a figure is wrong or out of date? Send a correction.