ConverterHub

Golden Ratio Calculator

Divide a total length into golden-ratio proportions.

How it is calculated

A length is divided in the golden ratio when the whole relates to the longer part in the same proportion as the longer part relates to the shorter one: total / longer = longer / shorter = φ, where φ = (1 + √5) / 2 ≈ 1.6180339. The tool takes the total length and returns longer = total / φ and shorter = total − longer, each rounded to two decimals. The longer part is about 61.8% of the total and the shorter about 38.2%. The unit is whatever you used for the total (cm, pixels, inches) and the total must be greater than zero. The ratio is a design guideline in layouts, framing and typography, not a rule, and the two rounded parts may differ from the total by a hundredth.

Worked example

Split a 100 cm board in the golden ratio. φ is about 1.618034, so the longer part = 100 / 1.618034 = 61.80 cm. The shorter part = 100 − 61.80 = 38.20 cm. As a check, 100 / 61.80 ≈ 1.618 and 61.80 / 38.20 ≈ 1.618, so both proportions match φ. In a 960 px wide layout the same method gives a main column of about 593 px and a sidebar of about 367 px.

Try this example →

Common mistakes

  • Entering one of the parts as the total; the input is the full length, and the tool then finds both parts.
  • Multiplying the total by 1.618 to find the longer part, which gives a value larger than the total instead of dividing by φ.
  • Using 1.6 or 1.5 as a rough φ in manual checks and being confused by small differences.
  • Assuming the golden ratio is always the best-looking proportion; it is a guideline, and many good layouts do not use it.
  • Mixing units, such as entering the total in metres and reading the parts as centimetres.

About this calculator

This calculator splits a given length into two segments whose ratio equals the golden ratio, φ ≈ 1.618 — the proportion where the ratio of the whole length to the larger segment equals the ratio of the larger segment to the smaller one, a self-similar relationship that has fascinated mathematicians since antiquity.

Designers, photographers and architects use the golden ratio to divide a composition, page layout, or building facade into proportions that are widely considered visually pleasing — it shows up in classical architecture, Renaissance art, logo design, and photo composition guides as an alternative to the simpler rule of thirds. This calculator does the arithmetic so a designer can go straight from a total width or height to the exact split point without working out the ratio by hand.

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