Golden ratio calculator
Split a segment in the ratio φ, or find the partner to a given size.
Fill in the fields and the result will appear here automatically.
Split mode divides a positive length into two parts in the golden ratio φ = (1+√5)/2. Partner mode solves a different problem: a known size a gives a larger neighbour aφ and a smaller one a/φ. Those two outputs have ratio φ²; each is separated from the input a by a factor φ. The constant is calculated in machine precision and rounded for display, not represented as an exact irrational number.
How it works
Formula and logic
φ = (1 + √5)/2 ≈ 1.618034. A segment is split so that the whole is to the larger part as the larger is to the smaller: the larger part is the length divided by φ. In partner mode the known size is multiplied and divided by φ, giving both of its neighbours in the series.
Example
A segment of 100 splits into 61.8034 and 38.1966 — their ratio equals the ratio of the whole to the larger part.
Fields and units
- What you need — list option
- Segment length — length unit
- Known size — length unit
How to use
- — Choose whether to split a segment or find a partner.
- — Enter the length you know.
- — Read both parts, or both sizes.
- — Use one common length unit for input and output, such as centimetres or pixels. No unit conversion occurs. In partner mode the two outputs are not parts of the original a.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- Euclid VI.30: division in extreme and mean ratio
- Limitation
- Positive lengths in one unit you choose. Split mode preserves the sum of parts; partner mode returns two neighbours of the original size. The golden ratio is a mathematical proportion and does not by itself guarantee composition quality.
FAQ
Why is φ not simply set to 1.618?
1.618 is only a rounded value. Calculating (1+√5)/2 keeps more machine digits but still approximates an irrational number. Check ratios with allowance for display rounding rather than requiring bit-for-bit equality.
How can I check the split is right?
Divide the whole by the larger part, and the larger by the smaller: both give the same number φ. That is the definition.
Where is the golden ratio actually used?
In layout and typography — picking a column width against a page, a heading size against body text, the proportions of a card. It is a compositional device, not a law of nature.
Is it related to the Fibonacci numbers?
Yes: the ratio of consecutive Fibonacci numbers tends to φ. That is why 34 and 55 are almost a golden pair, as the partner mode shows.