Golden Ratio Calculator

The golden ratio is one of the most famous numbers in mathematics, written with the Greek letter phi and equal to roughly 1.618. It describes a special way of dividing a length so that the whole relates to the larger part exactly as the larger part relates to the smaller part, a proportion that has been used for centuries in art, architecture, product design, logos, photography and typography because it tends to look naturally balanced. This calculator makes working with it effortless. Enter a single measurement and tell the tool whether that figure is the longer segment, the shorter segment or the whole length, and it instantly returns the other two values along with phi itself, so you can lay out a design, crop an image, size a layout or set up a composition in perfect golden proportion. It works in whatever unit you like, since the ratio is the same whether you are dealing with millimetres, pixels, centimetres or metres, which makes it just as handy for a web designer spacing a page as for a woodworker planning a cabinet or a student exploring the maths behind the spiral. The golden ratio also links to the Fibonacci sequence, where the ratio of each pair of neighbouring numbers creeps closer and closer to phi, and to the golden rectangle, which keeps its golden proportion even after you remove a square from it. Below the calculator you will find the exact formula, a clear worked example and the reasoning behind it, so you can understand the number rather than just use it, and apply it confidently in your own work.