Golden ratio calculator

Enter one length — the whole, the longer part or the shorter part — and get the other two so that whole : longer = longer : shorter = φ ≈ 1.618. Handy for layouts, type scales, picture framing and composition.

I know the
Longer part a61.803399
Shorter part b38.196601
Total a + b
100
Golden ratio φ
1.6180339887

Runs in your browser: nothing you enter is sent anywhere.

How to use it

  1. Choose which length you know: the total, the longer part or the shorter part.
  2. Enter it, in any unit.
  3. Read the other two lengths in the same unit.

Formulas

With φ = (1 + √5) / 2 ≈ 1.6180339887 and φ² = φ + 1 ≈ 2.618:

  • from the total T: longer = T / φ, shorter = T / φ²
  • from the longer part a: shorter = a / φ, total = a × φ
  • from the shorter part b: longer = b × φ, total = b × φ²

Worked example

A 1200 px wide layout split by the golden ratio: the main column is 1200 / 1.618034 = 741.6 px and the sidebar 458.4 px. Check: 741.6 / 458.4 ≈ 1.618.

Tips

  • 61.8 % and 38.2 % are the same split expressed as percentages of the total.
  • For a quick estimate, multiply by 0.618 for the longer part and by 0.382 for the shorter.

Frequently asked questions

What is the golden ratio?

The number φ = (1 + √5) / 2 ≈ 1.6180339887. Two lengths a > b are in the golden ratio when (a + b) / a = a / b = φ: the whole relates to the longer part as the longer part relates to the shorter.

How do I split a length by the golden ratio?

Divide the total by φ for the longer part, and subtract it for the shorter part. For 100: 100 / 1.618034 = 61.8034 and 100 − 61.8034 = 38.1966.

How do I find the other side of a golden rectangle?

Choose “Longer part” and enter the long side to get the short side (long ÷ φ), or choose “Shorter part” and enter the short side to get the long side (short × φ). A 10 cm short side needs a 16.18 cm long side.

How is it related to the Fibonacci numbers?

The ratio of consecutive Fibonacci numbers — 8/5, 13/8, 21/13 … — gets closer and closer to φ. That is why 5:8 or 8:13 are used as whole-number approximations.

More in Math

All tools in this category: Math ·Updated November 4, 2026

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