How recursive golden ratio splits are calculated
A golden ratio split rarely stops after one cut. In layout work the larger part is split again at the same ratio, then again, so you need the numbers for every stage rather than a single pair. Enter the total length and how many steps you want, and the table lists the larger part, the smaller part, the cut position measured from the origin, and the share the smaller part takes of the whole. One length is enough, whether it is a width or a height.
The formula is phi = (1 + sqrt 5) / 2 = 1.6180339887. At each stage the larger part is the remaining length times 0.6180339887 and the smaller part is whatever is left, so the two always add back to the length before the cut. Only the larger part carries into the next step. Choose whether the larger part sits at the start or the end and the cut positions accumulate in that direction. Values show two decimals and the formula is printed with the results. Phi is a mathematical constant, unchanged as of October 2026.
Splitting a length into just two parts is handled by a separate golden ratio calculator; this page only builds the recursive table. It does not suggest what to place in each region, because there is no recognized evidence that the golden ratio looks better on every screen. Deep step counts can push a segment below one pixel, so the smallest segment and the number of sub-pixel segments are shown alongside the table.
Frequently Asked Questions
Anything from 1 to 10 steps. Deeper splits can drop a segment below one pixel, so the smallest segment and the count of sub-pixel segments are shown with the results.
The remaining length is multiplied by 0.6180339887. The smaller part is the remainder, so adding the two returns exactly the length before that cut.
Adding the displayed values, which are rounded to two decimals, can be off by hundredths of a pixel. The internal calculation runs on unrounded values all the way through.