Golden Ratio Calculator

Enter just one length and instantly calculate the matching length at the golden ratio (about 1:1.618).

What is the golden ratio?

The golden ratio is approximately 1:1.618 β€” a special proportion where, when a whole length is split into two parts, "whole : long part = long part : short part" holds true. It's denoted by the Greek letter Ο† (phi), and its exact value is (1+√5)/2 β‰ˆ 1.6180339887...

Where is the golden ratio used?

A note on accuracy

The claim that the golden ratio is "the most beautiful proportion" hasn't been rigorously proven scientifically, and some instances are explained by coincidence or confirmation bias. Even so, it remains a widely referenced proportion in design and art.

Frequently Asked Questions

How is the Fibonacci sequence related to the golden ratio?

In the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...), the ratio between two consecutive numbers gets closer and closer to the golden ratio (1.618...) as the sequence grows. For example, 13Γ·8 = 1.625, which is very close to the golden ratio.

Is it exactly 1.618?

The golden ratio is an irrational number (it involves √5), so its decimal digits continue infinitely. 1.618 is a convenient approximation; the exact value is (1+√5)/2.