Golden Ratio Calculator

Use the Golden Ratio Calculator to calculate the Golden Ratio between two numbers. In this tutorial we explain how to calculate the golden ratio and explain, in clear steps, the concept of the golden ratio. Did You know? Many architects and artists believe that the golden ratio brings out the most beautiful and pleasant aesthetics.

Golden Ratio Calculator
Golden Ratio Calculator Results
The Ratio Numerator (a) is
The Ratio Denominator (b) is
The Sum of ratio values a+b (c) is
Golden Ratio Formula for calculating the Ratio Numerator
a/b = 1.618
a/ = 1.618
a = 1.618 ×
a =
Golden Ratio Formula for calculating the Ratio Denominator
a + b/a = 1.618
+ b/ = 1.618
+ b = 1.618 ×
+ b =
b = -
b =

Please rate this Ratio Calculator. If you are new to ratios or want to learn more about ratio calculations then we suggest you review our Introduction to Ratios with Supporting 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

Using the golden ratio equation, you get the value:

ɸ = 1 + √5/2
ɸ = 1.6180339887

Or

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 have one value from the ratio, either the numerator or the denominator. The other side of the ratio can be calculated using the Golden Ratio Formula. Here's how:

There are two separate formulas for calculating the Golden Ratio, one for calculating the ratio numerator and the second for calculating the ratio denominator, lets start by looking at how to calculate the ratio numerator using the Golden Ratio formula.

Golden Ratio Denominator Formula

a + b/a = 1.618

Calculating the Ratio Denominator using thr Golden Ratio Denominator formula

Suppose you choose 3 as the numerator part of the ratio.

If we consider our formula, we now have the known value of the numerator a = 3 and we need to calculate the value of the ratio denominator b using the rule of the golden ratio,

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

We know have our calculation for the ratio denominator using the Golden Ratio formula but, what if we need to calculate the ratio numerator using the golden ratio? We simply use the following Golden ratio formula:

Golden Ratio Numerator Formula

a/b = 1.618

In the previous example, we used the first method to find the value of b. In our next golden ratio example, the ratio numerator a is unknown and we have a ratio denominator value b = 3. We will use the second rule of the golden ratio to calculate our unknown ratio value:

Calculating the Ratio Numerator using thr Golden Ratio Numerator formula

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

The two formulas for calculating the Golden ratio and examples above will allow you to manually calculate the golden ratio, you can then check that you have completed your calculations correctly using the Golden Ratio Calculator.

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 requires one known value from a ratio pair to calculate the unknown ratio value using the relevant golden ratio equation. Full calculations for each formula are displayed side by side so you can understand how both parts of the formula work hand in hand, in addition we provide the sum of the two ratio values, display the golden ratio as a fraction and convert the golden ratio to a percentage.

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 the 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 spiralling patterns of flower seed heads, snail and nautilus shells, the examples are galore!

Conclusion

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.