Use this Golden Ratio Calculator to find the missing value in a golden-ratio proportion. Enter any one value and the calculator will work out the other values using the relationship (A + B) : A = A : B. You can also choose how many decimal places to show in the result.
How to Use the Golden Ratio Calculator
Enter one known value in any of the four boxes and click Calculate. The calculator will fill in the remaining values using the golden ratio.
You can choose between 0 and 12 decimal places from the dropdown.
For example, if you enter 10 as A, the calculator finds:
- A + B ≈ 16.18
- A = 10
- B ≈ 6.18
The relationship is:
(A + B) : A = A : B
What Is the Golden Ratio?
The golden ratio is a special mathematical proportion represented by the Greek letter φ (phi). Its value is approximately 1.6180339887.
In a golden-ratio proportion, the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller part.
Golden Ratio Formula
The golden ratio can be written as:
φ = (1 + √5) / 2
So:
φ ≈ 1.6180339887
For the proportion used in this calculator:
(A + B) / A = A / B = φ
This means that once one of the values is known, the other values can be calculated.
Frequently Asked Questions
What is a Golden Ratio Calculator?
A Golden Ratio Calculator finds the missing values in a proportion based on the golden ratio. It uses the relationship (A + B) : A = A : B.
What is the value of the golden ratio?
The golden ratio is approximately 1.6180339887.
Can I enter any one value?
Yes. Enter one positive value in any one of the four boxes. The calculator will calculate the remaining values.
What does A + B mean?
A + B represents the whole length or total value, while A and B represent the larger and smaller parts of the golden-ratio proportion.
How many decimal places can I use?
You can choose from 0 to 12 decimal places using the Round to dropdown.
Where is the golden ratio used?
The golden ratio is a mathematical concept that is also commonly discussed in areas such as design, architecture, photography, art, and page layouts.
What formula does this calculator use?
The calculator uses:
(A + B) / A = A / B = φ
where φ ≈ 1.6180339887.
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