Math
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, phi, equals (1 + sqrt(5)) / 2, approximately 1.618034. Two lengths are in the golden ratio when the larger divided by the smaller equals the sum of both divided by the larger. The proportion was studied in the Renaissance as the "divine proportion," and you can see it in modern logo and layout grids and in the seed-head spirals of sunflowers, which space new seeds at the golden angle of about 137.5 degrees.
How do you split a length using the golden ratio?
Divide the total length L by phi to get the longer segment: a = L / phi. The shorter segment is b = L - a. For L = 100, a is about 61.8034 and b is about 38.1966. The calculator does this in "From total" mode and rounds each result to six decimal places.
What is the inverse of phi?
1 / phi equals phi - 1, approximately 0.618034. That identity is unique to the golden ratio: subtracting 1 from phi gives the same value as dividing 1 by phi. The shorter segment divided by the longer segment always equals this inverse, 0.618034.
When are two numbers approximately golden?
The calculator marks two values as approximately golden when the ratio of the larger to the smaller is within 1% of phi, specifically when |a / b - phi| / phi is at most 0.01. That window covers ratios from about 1.602 to 1.634, which is close enough for most design and photography work.
Why is the golden ratio used in design?
A split at roughly 61.8% and 38.2% reads as naturally balanced to most viewers without feeling forced or symmetrical. Designers use it to size columns, set headline-to-body-text ratios, crop images, and position focal points in logos because the proportion carries visual weight without strict mathematical rigidity.