Golden Ratio Calculator

Design with the golden ratio

The golden ratio, written as the Greek letter phi (φ) and equal to about 1.618, is a proportion that appears throughout art, architecture, nature, and graphic design. Two lengths are in the golden ratio when the larger divided by the smaller equals the whole divided by the larger. Designers reach for it to size headings against body text, to set the proportions of a layout, and to build harmonious grids and spacing scales.

This calculator works two ways. In from a value mode, you enter one measurement and get its golden-longer counterpart (your value multiplied by φ) and its golden-shorter counterpart (your value divided by φ) — handy for building a type scale from a base font size, or finding a complementary width. In split a total mode, you enter a total length and it is divided into a long and a short part whose ratio is exactly φ and which add back up to the total — perfect for splitting a page, a sidebar, or a section into golden proportions.

FAQ

What is the golden ratio? It is the number φ ≈ 1.6180339887, the positive solution of φ = 1 + 1/φ. Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity.

How do I split a length by the golden ratio? Divide the total by φ to get the long part, then subtract that from the total to get the short part. The long part is about 61.8% of the total and the short part about 38.2%.

How is the golden ratio used in typography? Multiply a base font size by φ to get a larger heading size, or divide by φ for a smaller caption size, producing a balanced type scale where each step relates to the next by the same pleasing proportion.