Online calculator: Golden ratio

This calculator determines proportions according to golden ratio. You can read about the golden ratio below the calculator

Golden ratio

Length

Type

Calculation precision

Digits after the decimal point: 8

Long

Short

Sum

Golden ratio

Golden ratio also known as the divine proportion, golden mean, or golden section is a term for dividing a segment so the long/short ratio is equal to all/long ratio.
$\frac{a}{b}=\frac{a+b}{a}$
This number is constant.
If we suppose that b is 1, a should be equal to golden ratio. Let's substitute it for x
$\frac{x}{1}=\frac{x+1}{x}$
$x=\frac{x+1}{x}$
$x^2=x+1$
$x^2-x-1=0$

This is square equation. The positive root of the equation is
$\frac{1+\sqrt{5}}{2}$
and it is a golden ratio number
$\frac{\sqrt{5}+1}{2}=1,6180339887...$
It is irrational number.