Golden Ratio Calculator
This calculator solves the golden ratio from any one segment you already know. Tell it whether your number is the whole length, the longer part or the shorter part, and it fills in the other two so the whole divided by the longer equals the longer divided by the shorter. Results are rounded to four decimals and drawn as a proportion bar so you can see the split.
How to use the golden ratio calculator
- Open the 'I know the' dropdown and pick Whole length, Longer segment or Shorter segment.
- Type your measurement into the Value field.
- Read the three result cards labelled Whole, Longer and Shorter.
- Check the coloured bar below to preview the longer and shorter split.
- Use the Copy button on any card to grab that number for your design.
Examples
Split a 100px width (I know the whole)
I know the Whole length, Value = 100
Whole 100, Longer 61.8034, Shorter 38.1966
Grow from the longer part (I know the longer)
I know the Longer segment, Value = 100
Whole 161.8034, Longer 100, Shorter 61.8034
Build up from the shorter part (I know the shorter)
I know the Shorter segment, Value = 50
Whole 130.9017, Longer 80.9017, Shorter 50
Frequently asked questions
What is the golden ratio?
The golden ratio, written as the Greek letter phi, is approximately 1.618. Two lengths are in this ratio when the whole divided by the longer part equals the longer part divided by the shorter part.
Which value should I choose in the dropdown?
Pick the role of the number you already have. Choose Whole length to divide a total, Longer segment when you know the bigger piece, or Shorter segment when you know the smaller piece and want to build outward.
How does it split a whole length?
It divides your whole by phi to get the longer segment, then subtracts that from the whole to get the shorter segment. For a whole of 100 the longer part is 61.8034 and the shorter part is 38.1966.
How does it work backwards from a segment?
If you enter the shorter part it multiplies by phi to find the longer part and adds the two for the whole. If you enter the longer part it divides by phi for the shorter part and adds them for the whole.
Why are the answers rounded to four decimals?
Phi is irrational, so the results never terminate. The tool rounds each figure to four decimal places, which is precise enough for layout, print and screen work while keeping the numbers readable.
What does the coloured bar show?
It is a live preview of the split. The darker indigo block represents the longer segment and the lighter block the shorter, sized in proportion to the two results so you can eyeball the balance.
Can I use any unit?
Yes. The calculator is unit agnostic, so a value of 100 works the same whether you mean pixels, millimetres, points or inches. Just keep the same unit in mind for all three results.
Is phi the same as the Fibonacci sequence?
They are closely linked but not identical. The ratio of two consecutive Fibonacci numbers gets closer and closer to phi as the numbers grow, so Fibonacci is a whole-number approximation of the same proportion.
Is anything uploaded when I calculate?
No. Every calculation runs in your browser and nothing is sent to a server, so your measurements stay entirely on your device.
Learn more
- Using the golden ratio in layout and typography
Practical ways to apply phi to grids, columns, image crops and type sizes, plus the honest limits of the divine proportion.
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