Golden Ratio Calculator
Split a length using the golden ratio phi (1.618...). Solve from total, longer, or shorter part and see the exact a:b:L breakdown.
Golden ratio split
Enter a positive total length. It splits into longer = L / phi and shorter = L - longer.
Golden split
61.8034:38.1966
Longer (a) and shorter (b), with a / b = phi.
- Total (L = a + b)
- 100
- Longer (a)
- 61.803399
- Shorter (b)
- 38.196601
- phi
- 1.618034
- 1 / phi
- 0.618034
- a / b
- 1.618034
L / a = a / b = phi
100 / 61.8034 = 61.8034 / 38.1966 = 1.618
Approximately golden (within 1% of phi).
Frequently Asked Questions about the Golden Ratio Calculator
What is the golden ratio?
The golden ratio, written phi, equals (1 + sqrt(5)) / 2, about 1.6180339887. Two quantities are in the golden ratio when the larger divided by the smaller equals the sum divided by the larger. It shows up in art, architecture, design layouts, and nature.
How do you split a length using the golden ratio?
Divide the total length L by phi to get the longer part: a = L / phi. The shorter part is what remains: b = L - a, which also equals L times (phi - 1) / phi. For L = 100, a is about 61.803 and b is about 38.197.
What is the inverse of phi?
1 / phi equals phi - 1, about 0.6180339887. That identity is unique to the golden ratio and is why the shorter part divided by the longer part gives the same digits as phi minus 1.
When are two numbers approximately golden?
When the ratio of the larger to the smaller is within about 1% of phi. This calculator flags inputs as approximately golden whenever |a / b - phi| / phi is at most 0.01, which covers most design and photography use cases.
Why is the golden ratio used in design?
Layouts split at roughly 61.8% and 38.2% feel naturally balanced to most viewers. Designers use it to size columns, crop photos, set typography scales, and lay out logos because the proportions read as harmonious without looking mathematically rigid.