HesapHanem

Golden Ratio Calculator

Divide a total length into golden-ratio proportions.

Result

61.80
38.20

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.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    If you know the shorter part and need the whole, the tool will not run that direction, but you can do it by hand: multiply the shorter part by 2.618 (φ squared) for the total, or by 1.618 for the longer part. With 38.2 that gives about 100 and 61.8. Results carry two decimals, so for pixels or millimetres round to whole numbers before cutting or placing anything. What are you laying out with it: a page, a photo crop or a piece of furniture?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators