Golden ratio calculator

Split a total length in the golden ratio φ = (1 + √5)/2.

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Total length

Answer

…

Split a total length in the golden ratio φ = (1 + √5)/2.

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Precision and calculation record

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Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

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Formula and assumptions

The longer divided by the shorter equals the whole divided by the longer. This is a mathematical proportion, not a claim about aesthetic preference.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Golden ratio calculator

Split a total length in the golden ratio φ = (1 + √5)/2.

The longer divided by the shorter equals the whole divided by the longer. This is a mathematical proportion, not a claim about aesthetic preference.

Next: Ratio calculator

A worked example

Example inputs: total length = 10. Longer segment = 6.1803398875.

Before you use the result

The longer divided by the shorter equals the whole divided by the longer. This is a mathematical proportion, not a claim about aesthetic preference.

Example results for total length

These examples use the formula above. They are reference calculations, not recommended settings.

Total length	Longer segment
5	3.09016994375
10	6.1803398875
20	12.360679775

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ToolOctopus. “Golden ratio calculator.” Updated 2026-09-26. https://tooloctopus.com/golden-ratio-calculator.

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