Golden Ratio Calculator

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.

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.

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.

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.

The golden ratio offers one reusable proportion for grids, columns, crops, and type scales. It can create consistent relationships between dimensions, but there is no universal evidence that a 61.8% to 38.2% split is inherently more pleasing than other well-composed proportions. Treat it as an optional design tool, not a rule.