Golden Ratio Calculator
This golden ratio calculator starts from any of the three dimensions: the whole length, the long part or the short part. For 100 cm you get 61.8 cm and 38.2 cm – the ratio of the two parts equals the ratio of the whole to the long part, which is 1.618.
Example: You know: the whole length · Measurement 100 · Unit: cm → Result: Long part: 61.803 cm · short part: 38.197 cm. Source: Wikipedia – Goldener Schnitt (Definition, Φ = (1+√5)/2). Updated: .
How it is calculated
In the golden ratio the long part of a line relates to the short part as the whole line relates to the long part. That ratio is the irrational number Φ = (1 + √5) ÷ 2 ≈ 1.6180339887. The long part is about 61.8% of the whole length and the short part about 38.2%.
How the tool works
- Whole length known: long part = whole ÷ 1.618; short part = whole − long part.
- Long part known: whole = long part × 1.618.
- Short part known: long part = short part × 1.618 and whole = short part × 2.618 (that is Φ²).
The same figures give a golden rectangle: cut off a square and what is left is again a golden rectangle, and so on indefinitely.
What is it used for?
In design, photography and architecture it serves as a guide to pleasing proportions: dividing images and page layouts, sizing mats and shelves, planning furniture or garden beds. The ratio of consecutive Fibonacci numbers approaches it – 55 ÷ 34 is already 1.6176; see the sequence calculator. For other shapes use the rectangle calculator. Whether the golden ratio really looks “better” is disputed in research, but it remains a handy rule of thumb.
Frequently asked questions
What is the golden ratio?
A division in which the longer part relates to the shorter part as the whole relates to the longer part. The ratio is Φ ≈ 1.618, roughly 61.8% to 38.2%.
How do you calculate the golden ratio?
Divide the whole length by 1.618 to get the long part; the remainder is the short part. For 50 cm that is 30.9 cm and 19.1 cm.
How do I divide a board or wall in the golden ratio?
Measure the whole length, multiply by 0.618 and mark that distance from one end. The calculator does the arithmetic.
What is the difference between major and minor?
The major is the longer part of the line and the minor the shorter one. Major ÷ minor equals the golden ratio.
How are the golden ratio and Fibonacci numbers related?
Divide two consecutive Fibonacci numbers, such as 89 ÷ 55, and the result gets closer and closer to 1.618.
Sources and legal basis
- Wikipedia – Goldener Schnitt (Definition, Φ = (1+√5)/2)
- Wikipedia – Golden ratio
- OEIS A001622 – decimal expansion of the golden ratio
As of: · Editorial policy
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