Two lengths are in the golden ratio when the whole relates to the larger part as the larger part relates to the smaller.
How to use the Golden Ratio Calculator
- Total length
- Want to work backwards? Type a value into Longer part and Total length is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Divide the total by φ for the longer part; the remainder is the shorter part.
What each result means
- Longer part = [Total length] ÷ ((1 + sqrt(5))÷2)
- Shorter part = [Total length] – [Longer part]
- Golden extension of total = [Total length] × (1 + sqrt(5))÷2
Example values
How the main result changes when Total length changes and everything else stays at the example values above:
| Total length | Longer part |
|---|---|
| 50 | 30.9017 |
| 75 | 46.3525 |
| 100 | 61.8034 |
| 125 | 77.2542 |
| 150 | 92.7051 |
| 200 | 123.6068 |
Formula
φ = (1 + √5) ÷ 2 ≈ 1.6180339887Worked example
Inputs — Total length: 100.
Results — Longer part = 61.803399; Shorter part = 38.196601; Golden extension of total = 161.803399.
Frequently asked questions
Is the golden ratio really everywhere in nature?
It appears in some patterns, but many claims are exaggerated.
How is it linked to Fibonacci?
Ratios of consecutive Fibonacci numbers approach φ.
What formula does the Golden Ratio Calculator use?
φ = (1 + √5) ÷ 2 ≈ 1.6180339887.
Can I work backwards from the result?
Yes. Type the result you want into Longer part and the calculator finds the matching total length.