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Golden Ratio Calculator

Free online tool that helps you calculate the length of the line segments and the entire line in the Golden ratio.

Line segment
Shorter part
Longer part

What is the Golden ratio?

The Golden ratio, also known as the divine proportion, is a mathematical constant that has been studied for thousands of years. It is denoted by the Greek letter phi (φ) and has a value of approximately 1.6180339887.

The Golden ratio appears in many different areas of mathematics, science, and art. It is often found in natural objects and structures, such as the spiral patterns of shells, the branching patterns of trees, and the proportions of the human body.

In art, the Golden ratio is often used to create pleasing and harmonious compositions. It is a proportion that is said to be aesthetically pleasing to the eye, and has been used by many artists and architects throughout history.

The Golden ratio can be found by dividing a line into two parts so that the longer part divided by the smaller part is equal to the whole length divided by the longer part. This creates a ratio of approximately 1.618, which is the Golden ratio.

How to calculate golden ratio?

The Golden ratio can be calculated in several ways. One of the simplest ways to calculate the Golden ratio is through the following formula:

φ = (1 + √5) / 2

To use this formula, simply add 1 to the square root of 5 and then divide the result by 2. The resulting value will be the Golden ratio, which is approximately equal to 1.6180339887.

Another way to calculate the Golden ratio is through the Fibonacci sequence. In this sequence, each number is the sum of the two preceding numbers. As the numbers in the Fibonacci sequence get larger, the ratio of each number to its predecessor approaches the Golden ratio. For example, as the Fibonacci sequence gets larger, the ratio of 13 to 8 is approximately equal to 1.625, which is very close to the Golden ratio.

These are just a couple of ways to calculate the Golden ratio, but there are many other methods that exist as well.

What is a golden rectangle?

A Golden rectangle is a rectangle whose length and width are in the Golden ratio, which is approximately 1.6180339887. This ratio is also known as the Golden mean or divine proportion.

A Golden rectangle has the unique property that if you remove a square from it, the remaining rectangle is also a Golden rectangle. This property can be repeated indefinitely, creating a series of Golden rectangles that get smaller and smaller.

The proportions of Golden rectangles have been found to be aesthetically pleasing and are often used in art, design, and architecture. For example, many famous buildings, such as the Parthenon in Athens and the Notre-Dame Cathedral in Paris, were designed using Golden rectangles. In addition, many artists, such as Leonardo da Vinci and Salvador Dali, incorporated Golden rectangles into their work to create balance and harmony.

To create a Golden rectangle, you can start with a square and then extend one of its sides to create a longer rectangle. The length of the longer side should be 1.618 times the length of the shorter side.