# Golden Ratio Calculator

Enter one of the known values to calculate the other values in a golden ratio.

## Results:

Segment (a): | |

Segment (b): | |

Sum (a + b): |

## On this page:

## How to Solve the Parts of a Golden Ratio

The golden ratio, also known as the golden section or golden mean, is the ratio between the sum of two values *(a + b)* to value *a* being the same as the ratio between value *a* and value *b*.

The golden ratio is expressed using the Greek letter φ, or phi.

Thus, the golden ratio can be expressed as:

a + b / a = a / b = φ

Thus, *(a + b)* is to *a* as *a* is to *b*. This special ratio is actually derived from the Fibonacci sequence.

The golden ratio can also be expressed using the formula:

φ = 1 + √5 / 2 ≈ 1.618

Thus, the golden ratio φ is equal to 1 plus the square root of 5, divided by 2, or approximately 1.6180327868852. Put more simply, the golden ratio is roughly equal to **1.618**.

So, how do you solve values that are part of a golden ratio?

### How to Solve for a

If the value *b* is known, then the following formula can be used to solve for value *a* if the ratio between them is the golden ratio.

a = b × φ

So, *a* is equal to *b* times 1.618.

### How to Solve for b

If the value *a* is known, then the following formula can be used to solve for value *b* if the ratio between them is the golden ratio.

b = a / φ

So, *b* is equal to *a* divided by 1.618.