Golden Ratio Calculator

To compute the golden ratio, use the golden ratio calculator to determine the shorter side, long side, and the combined length of the two sides. It's critical to understand what the golden ratio is before we can calculate it. Read the further sections to learn what is meant by Golden Ratio, How to Compute Golden Ratio by hand, What is meant by Golden Rectangle, etc. in the further modules.

Calculation With:
Longer section (A)

You may set the number of decimal places in the online calculator. By default there are only two decimal places.

Round Upto:

What is the Golden Ratio?

The golden ratio, also known as the golden section or golden proportion, is obtained when the percentage of two segment lengths to the bigger of the two lengths is the same. The golden ratio has a value of about 1.618, which is the limit of the ratio of consecutive Fibonacci numbers.

The golden ratio is calculated using the following formula. Let's call the larger of the two pieces a, and the smaller b. As a result, the golden ratio is (a+b)/a = a/b. Any old ratio calculator will do the task, but this golden ratio calculator is specifically designed to cope with this issue, so you don't have to worry!


How to solve the Golden Ratio by Hand?

  • Step 1: Locate the longest segment and give it a name.
  • Step 2: Find the shorter part and name it with the letter b.
  • Step 3: Fill in the blanks in the formula.
  • Step 4: Divide the sum of a and b by a.
  • Step 5: Take a and divide it by b.
  • Step 6: The golden ratio equals around 1.618 if the proportion is in the golden ratio.
  • Step 7: To double-check your answer, use the golden ratio calculator.

When three points are collinear and two of the distances are known, the segment addition postulate can be used to find one of the segment lengths.


How to use Golden Ratio Calculator?

Find values that satisfy the golden ratio using this calculator, where (A+B):A = A:B. To calculate the missing golden ratio values, enter any ratio term. Based on the golden ratio formula, the solution also includes two more, equivalent sets of golden ratio terms.

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What is a Golden Rectangle?

The golden rectangle has a length of a + bandwidth of a. This rectangle is frequently depicted in art because it is regarded to be the most appealing to the sight of all rectangles. Instead of working it out by hand, you can use the golden rectangle calculator. Many styles of architecture and even natural patterns, such as the arrangement of leaves in some plants, use the golden ratio. Regular pentagons have the golden proportion as well.


FAQs on Golden Ratio Calculator

1. What is the Golden Ratio?

The golden ratio also called the golden mean, is defined as phi = (A+B)/A = A/B.


2. What is the formula for calculating the Golden Ratio?

When you divide a line into two parts, you get the Golden Ratio when the longer part (a) divided by the smaller part (b) equals the sum of (a) + (b) divided by (a), which equals 1.618.


3. What is the Golden Rectangle formula?

The golden rectangle is a rectangle with sides that are in the golden ratio, i.e. (a + b)/a = a/b, where an is the width and a + b is the length.


4. What happens if the golden ratio is reduced by one?

The golden ratio is the only integer whose square can be obtained by adding one and whose reciprocal can be obtained by removing one. When you snip a square out of a golden rectangle (one whose length-to-breadth ratio is in the golden ratio), you get another, smaller golden rectangle.


5. What is the significance of 1.618?

The Golden Ratio (phi = φ) is often referred to as the Universe's Most Beautiful Number. The reason it is so remarkable is that it can be pictured practically anywhere, starting with geometry and ending with the human body! This was dubbed "The Divine Proportion" or "The Golden Ratio" by Renaissance artists.