Golden Ratio Calculator | Math Calculators | iCalculator

Calculate the Golden ratio between two numbers. To know how a golden ratio calculator works, we need to understand the concept of the golden ratio. Many architects and artists believe that the golden ratio brings out the most beautiful and pleasant picture.

Golden Ratio Calculator
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Golden Ratio Calculator. This image shows Golden Ratio formula with associated calculations used by the Golden Ratio Calculator

What is the Golden Ratio

Denoted by the Greek symbol ɸ (phi), the golden ratio is a mathematical concept where the two parts of a ratio are divided in such a way that:

(a+b)/a = a/b = ɸ

Mathematically, the golden ratio is an irrational number we get after solving the following quadratic equation:

ɸ = x² - x - 1 = 0

Solving the above equation, you get the value:

ɸ = (1 + √5)/2
ɸ = 1.6180339887


ɸ = 1.62

The golden ratio is also known as the mean ratio, extreme ratio, medial section, Sectio Divina (divine section), golden number, golden cut, golden proportion, and divine proportion.

In layman terms, we can exemplify the golden ratio as a line divided into two sections such that:

  • The long section divided by the short path

Is equal to

  • The whole line divided by the long section

If a line segment of 10cm is to be divided into the golden ratio, the long part will be 6.12cm while the short part will be 3.82cm in their respective lengths.

At the same time, if you want to draw a rectangle ABCD with length 10cm, the width of such a rectangle will be 6.18.

How to calculate the Golden Ratio Manually

In most cases, the golden ratio is used to make artistic or architectural beauties, and thus, the key lies in knowing how to reach the golden ratio. Since the number itself has a fixed value, all we need is two choose one side of the ratio. The other one can be calculated easily. Here's how:

Suppose you choose 3 as the small part of the ratio. Now, there are two ways to find the dimensions of the other line:

If 3 is the greater part of the golden ratio

In such a case, a=3 and we need to find b because by rule of the golden ratio,

(a+b)/a = 1.618.


(3+b)/3 = 1.618
3 + b = 3 x 1.618
3 + b = 4.854
b = 4.854 - 3
b = 1.854
a = 3, b = 1.854

Furthermore, a/b = 1.618

If 3 is the smaller part of the golden ratio

In the previous example, we used the first method to find the value of b. In this case, a is unknown and we have b = 3. We will use the second rule of the golden ratio to find out the value of a here. According to the golden ratio rule,

a/b = 1.618
a/3 = 1.618
a = 1.618 x 3
a = 4.854

How to use the Golden Ratio Calculator

The golden ratio calculator developed by iCalculator is an extremely easy to use online calculator. This ratio calculator simply takes one step to find out the golden ratio along with the sum of the two ratio terms.

Depending upon whether you have the value of the large portion, or the smaller one you simply need to enter the given value as "a" or "b". After that, all you need to do is click the "Calculate" button.

The two examples mentioned above where 3 is the larger and smaller value, we used the golden ratio calculator to give you the right results. Just like all our other digital calculators, we tested the final version of the golden ratio calculator and compared its results with a scientific calculator.

Use of Golden Ratio in Real Life

Renowned Swiss architect, Le Corbusier (1887 - 1965) was known for his love for proportions and structural harmony. He strongly believed that the universe has a mathematical order which is closely related to the Fibonacci series and the golden ratio.

At the same time, Salvador Dali, one of the greatest artists in history also loved to work around the concept of the golden ratio. Almost all of his works in landscape orientation are created on the golden rectangle, a geometric shape that is based on the golden ratio.

The golden ratio is also present in nature, you simply need to look at the base of the pine cones, the spiraling patterns of flower seed heads, snail and nautilus shells, the examples are galore!


As we can see from the two examples above, the greatest of architects and artists loved to work with the golden ratio, and many still do. The golden ratio gives a picturesque finish to buildings and paintings. While you may need to work with the golden ratio only for your homework or an assignment, there are many practical applications too. And all you need is the golden ratio calculator, brought to you by iCalculator.

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