Given one dimension, this finds the other dimension in golden-ratio proportion — a ratio long associated with pleasing visual composition in art and design.
How it works
Multiplying the smaller part by phi (approximately 1.618) gives the larger part; dividing the larger part by phi gives the smaller part back.
What this does not include
This does not include Fibonacci sequence generation, a related but distinct mathematical concept that approximates the golden ratio as the sequence progresses.
How to use this calculator
- Choose which part you know, then enter its value.
A worked example
Given a smaller segment of 10, the larger segment that forms the golden ratio is 10 × φ = 16.1803 (φ ≈ 1.6180339887).
Given a larger segment of 16.1803398875, the smaller segment works out to 10 — the reverse calculation.
What the variables mean
| Variable | Meaning |
|---|---|
| Smaller segment | The shorter of the two lengths |
| Larger segment | The longer of the two lengths |
| φ (phi) | The golden ratio constant, approximately 1.618 |
Edge cases worth knowing
A segment of zero makes the ratio meaningless — the golden ratio describes a proportion between two positive lengths, and zero breaks that proportion entirely.
The golden ratio is irrational — its decimal expansion never terminates or repeats, so any displayed value is necessarily a rounded approximation of φ.
Frequently asked questions
What exactly is the golden ratio?
An irrational number, approximately 1.618, defined so that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part.
Where is the golden ratio used?
Design, architecture, and art composition, where proportions close to the golden ratio are often considered visually balanced.
Is the golden ratio related to the Fibonacci sequence?
Yes — the ratio of consecutive Fibonacci numbers approaches the golden ratio as the sequence progresses further.
