What the golden ratio is
Divide a line so that the whole is to the longer part as the longer part is to the shorter. That proportion is 1.6180339887, written as the Greek letter phi.
It is the positive solution of x squared equals x plus 1, which is where the number comes from.
Worked example
A shorter part of 10 gives a longer part of 16.18034, because 10 x 1.618034 is 16.18034.
The two parts together make 26.18034, and the longer divided by the shorter is 1.618034 again.
Checking a pair
Divide the larger length by the smaller. If the answer is within about one hundredth of 1.618034, the pair is close to the golden ratio.
Real measurements are rarely exact, so the verdict allows for rounding in whatever you measured.
Inputs for the golden ratio calculator
What do you want to do?
Find the partner of one length, or check a pair you already have.
Shorter part
The length you have, which becomes the shorter part of the pair.
First and second length
The two lengths to compare. The order does not change the ratio.
CALCULATOR QUESTIONS
Golden ratio calculator questions
What is the golden ratio?
About 1.618034. Two lengths are in it when the longer divided by the shorter gives that number.
If the shorter part is 10, what is the longer part?
16.18034, because 10 multiplied by 1.618034 is 16.18034.
Are 10 and 16.18 in the golden ratio?
Very close. The ratio is 1.618, within a hundredth of 1.618034, so the calculator accepts the pair.
Where is the golden ratio used?
In art, design and geometry, and in mathematics it appears in the Fibonacci sequence and in regular pentagons.