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Golden Ratio Calculator

Split a length by the golden ratio, or find the matching longer or shorter part, for design, photography and layout.

Rules last checked 10 November 2026Every step shown

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Any unit: cm, pixels, inches. The answers use the same one.

Longer part

61.8034

Shorter part
38.1966
Whole length
100
Next size up (whole × φ)
161.8034

From the whole of 100: the longer part is 61.803 and the shorter 38.197, so the whole is 100. Whole ÷ longer and longer ÷ shorter both equal 1.618.

How it's worked out

  1. Golden ratio φ(1 + √5) ÷ 21.618034
  2. Longer part100 ÷ 1.61861.8034
  3. Shorter part100 − 61.803438.1966
  • φ is about 1.618. Dividing by it is the same as multiplying by 0.618, which is how designers often split a page or a photo.

How it is worked out

The longer part is the whole ÷ 1.618, and the shorter part is the whole minus the longer part. Starting from the longer part, the shorter is longer ÷ 1.618; from the shorter, the longer is shorter × 1.618.

Questions people ask

How do I split 100 by the golden ratio?

Into 61.8 and 38.2. 100 ÷ 61.8 and 61.8 ÷ 38.2 both come to about 1.618.

What is the golden ratio?

About 1.618, written φ (phi). It's (1 + √5) ÷ 2: the ratio where the whole compares to the longer part as the longer part compares to the shorter.

How do designers use it?

To split a page, a photo or a layout into two parts that look balanced, such as a main column 61.8% wide and a sidebar 38.2% wide.

How is it linked to the Fibonacci sequence?

Dividing each Fibonacci number by the one before (8 ÷ 5, 13 ÷ 8, 21 ÷ 13…) gets closer and closer to 1.618.

Formula and rules last checked 10 November 2026Written and tested by the CalculatorDex teamReport a problem