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Golden Ratio Calculator

Work out golden ratio instantly with clear inputs, formula shown and shareable results.

About Golden Ratio Calculator

The golden ratio φ = (1 + √5)/2 ≈ 1.6180340 is the unique number where the whole is to the longer part as the longer part is to the shorter. It satisfies φ² = φ + 1 and 1/φ = φ − 1.

Formulas

Golden ratio

φ = (1 + √5) / 2, φ² = φ + 1

Golden section

(a + b) / b = b / a = φ

Worked example

With the default values below, Golden Ratio Calculator returns Longer segment of 16.18033989. Change any input above and every figure here is recalculated in your browser.

Inputs used

Shorter length aminimum 0
10
Given length is theone of shorter segment, longer segment, whole length
shorter segment

Results

Longer segment
16.18033989
Shorter segment
10.00000000
Whole length
26.18033989
Golden ratio φ
1.6180339887

Step by step

  1. 1Values used
  2. 2Golden ratio
  3. 3Golden section
  4. 4Longer segment= 16.18033989
  5. 5Shorter segment= 10.00000000
  6. 6Whole length= 26.18033989
  7. 7Golden ratio φ= 1.6180339887

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

If the shorter part is 10?

The longer part is 16.180340 and the whole is 26.180340.

How is φ related to Fibonacci?

Consecutive Fibonacci ratios converge to φ: 8/5 = 1.6, 13/8 = 1.625, 21/13 ≈ 1.6154, and so on.

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