## Introduction to the Golden Ratio Calculator

Golden Ratio Calculator is a powerful tool that is designed to help you understand the mathematical concept of the golden ratio. Our tool **determines the ratio** between two quantities by keeping them equal according to the golden ratio equation.

## What is the Golden Ratio?

Golden ratio is defined as a special ratio in which two quantities are involved where the **ratio sum of one larger quantity** to the ratio of another quantity. It is often denoted by the Greek letter phi (φ), which is a mathematical constant. It is approximately equal to 1.61803398875.

Mathematically, the golden ratio can be defined in several ways:

a and ๐, the golden section can be expressed as

$$ ๐ + ๐๐ \;=\; \frac{๐}{๐} $$

Golden ratio can be seen in various contexts in nature, art, architecture, and mathematics. It is often associated with proportions and the dimensions of many natural objects, like in seashells, flowers, and even in human faces.

## Formula of the Golden Ratio:

Mathematically, the **formula of the golden ratio** can be expressed using the following formula in which a+b is the sum of the ratio and 1/a is another ratio. The formula used by the Golden Ratio Calculator to solve golden ratio problems is,

$$ \frac{a}{b} \;=\; \frac{a + b}{a} \;=\; 1.618 … \;=\; \emptyset $$

Therefore, any value of a, b in the divine proportion calculator’s calculation only gives an approximation value for the golden ratio.

## How to Calculate the Golden Ratio?

The golden ratio can be calculated in various ways, but one of the most **common methods** is the Fibonacci sequence. Here's how the magic ratio calculator calculates the approximate value of the golden section using the Fibonacci sequence:

- Golden mean calculator starts with the Fibonacci sequence, in which it takes two supposed values to get 2 and 1 then takes the sum of 0 and 1 which becomes 2+1=3. You can choose any consecutive quantity sequence of Fibonacci numbers which is 1,1,2,3,5,8,......
- Then golden section ratio calculator divides the smaller number by the larger number ½ because a is always greater than the quantity of b. You get solution ½ is 0.5.
- As you can see the sum value is not closely or equal to other quantity approx number. If a number is not equal to the approximate value then the golden cut calculator again takes another value.
- Divine proportion calculator repeats this process until the approximate sum and division values are the same.
- As you continue further along the Fibonacci sequence, the ratio of consecutive numbers approaches the golden section and gets an accurate value.

Another method used by the golden mean ratio calculator to calculate golden ratio number is algebraically:

- Solve the quadratic equation ๐ฅ
^{2}=๐ฅ+1 to find the roots φ. - φ
^{2}=φ+1 and φ=1/φ - The φ is always positive in the equation which is known as the golden ratio, which is approximately equal to 1.61803398875.

These are just a couple of methods to calculate the golden ratio number. Still, it is necessary to note that the value φ which is irrational, meaning it cannot be expressed exactly as a fraction or finite decimal.

## Practical Example of a Golden Ratio

Let's see a practical **example of the golden section** problem to understand the working procedure of the Golden ratio calculator.

### Example:

Find the golden ratio of a given table.

$$ n \;=\; 0 \; 1 \; 2 \; 3 \; 4 \; 5 \; 6 \; 7 \; 8 \; 9 \; 10 \; 11 \; 12 \; 13 \; 14 … $$

$$ x_n \;=\; 0 \; 1 \; 1\; 2\; 3 \; 5\; 8 \; 13\; 21 \; 34\; 55\; 89\; 144\; 233\; 377… $$

**Solution**:

\begin{matrix} A & B & B/A \\ 2 & 3 & 1.5 \\ 3 & 5 & 1.666666666… \\ 5 & 8 & 1.6 \\ 8 & 13 & 1.625 \\ … & … & … \\ 144 & 233 & 1.618055556 \\ 233 & 277 & 1.618025751 \\ … & … & … \\ \end{matrix}

Let’s randomly choose 192 and 16 to get the sequence,

\begin{matrix} A & B & B/A \\ 192 & 16 & 0.08333333… \\ 16 & 208 & 13 \\ 208 & 224 & 1.07692308… \\ 224 & 432 & 1.92857143… \\ … & … & … \\ 7408 & 11984 & 1.61771058… \\ 11984 & 19392 & 1.61815754… \\ … & … & … \\ \end{matrix}

Use the golden ratio to determine the Fibonacci numbers,

$$ x_n \;=\; \frac{(\phi^n - (1- \phi^n)}{\sqrt{5}} $$

After calculation solution will be the whole number which is equal to the division 1/a and sum (a+b) solution.

## Guide to Use Golden Ratio Calculator:

The magic ratio calculator has a simple design tool that enables you to use it to calculate two consecutive numbers with quadratic or Fibonacci methods.

Before entering the input function into the golden mean calculator, **follow some simple steps** so that you get a smooth experience. These steps are:

- Enter the larger number ‘a’ in the input box of the golden ratio converter.
- Enter the second number b in the input box.
- Enter the whole number (a+b) in the golden cut calculator’s input box.
- Review your consecutive number before hitting the calculate button to start the evaluation process.
- Click the “Calculate” button to get the result of your given golden ratio number problem.
- If you want to try out our golden section ratio calculator for the first time then you can use the load example to get a better understanding.
- Click on the “Recalculate” button to get a refresh page for more solutions to golden ratio number problems.

## Outcome of Magic Ratio Calculator

Golden ratio Calculator gives you the solution to a given question when you add the input into it. It provides you with solutions with a detailed procedure. It may contain as:

**Result option**

When you click on the Result option it gives you a **solution for the two quantities** to find the given problem

**Possible steps**

It provides you with a solution in which all the evaluation processes are present in a step-by-step method of the golden ratio number problem when you click on this option.

## Benefits of Using the Golden Mean Calculator

Divine proportion calculator provides you with multiple benefits whenever you use it to calculate different quantity problems and gives you approx value as a solution. These benefits are:

- The golden mean ratio calculator is a
**free-of-cost tool**that enables you to use it anytime to find the golden ratio problem in real time. - It is an adaptable tool that allows you to get the solution of different kinds of quantities for the golden ratio.
- You can try out our magic ratio calculator to practice more examples of consecutive quantities so that you get a strong hold on the perfect ratio concept.
- Our tool saves the time that you spend on doing complex calculations of consecutive number problems that give approx values.
- The golden cut calculator is a trustworthy tool that provides you with accurate solutions whenever you use it to calculate golden ratio examples without any man-made error.
- Golden ratio calculator provides the solution with a complete process in a stepwise method so that you get clarity on the different numbers problem.