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Golden Ratio Calculator

Divide or extend any length using the golden ratio.

  • Free
  • No sign-up
  • Nothing is sent or stored

Result

Longer part (a) · shorter part (b)
61.8034 · 38.1966
Whole (a + b)
100
Golden ratio φ
1.6180339887
Golden rectangle for width a
61.8 × 38.2
Next larger in the sequence
100
How it was calculated
  1. φ = (1 + √5) ÷ 2 ≈ 1.6180339887
  2. a ÷ b = (a + b) ÷ a = φ

The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved.

How to use the Golden Ratio Calculator

  1. Enter a length.
  2. Choose whether it's the whole, the longer part or the shorter part.
  3. Read the other lengths.

What does this tool do?

Two lengths are in the golden ratio when the larger divided by the smaller equals the whole divided by the larger — about 1.618, written φ (phi). Designers use it for pleasing proportions in layouts, grids and logos.

It's closely linked to the Fibonacci sequence: dividing consecutive Fibonacci numbers gives values ever closer to φ.

Why use it?

  • Any starting length.
  • Golden rectangle sizes.
  • Formula shown.

Privacy

The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.

Last reviewed by the M2Toolkit team.

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