Golden Ratio Calculator

The Golden Ratio Calculator is a tool that determines proportions according to the golden ratio. The user inputs a value and selects its type: long member, short member, or sum. The calculator then computes the other members of the golden ratio based on the input.

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Created: 2011-06-19 22:06:58, Last updated: 2023-04-04 16:52:26

The golden ratio, also known as the divine proportion, is a mathematical concept that appears in nature and art. It is a ratio of two quantities where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. This ratio is approximately equal to 1.61803398875, and it appears in many natural phenomena, such as the spiral pattern of shells and the branching pattern of trees. You can read more below the calculator.

PLANETCALC, Golden ratio

Golden ratio

Digits after the decimal point: 8
Golden ratio

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.
This number is constant.
If we suppose that b is 1, a should be equal to golden ratio. Let's substitute it for x

This is square equation. The positive root of the equation is
and it is a golden ratio number
It is irrational number.

The rough approximation of the golden ratio is the long part is 0,62 of all, and the short part is 0,38.

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PLANETCALC, Golden Ratio Calculator