Golden Rectangle Calculator

Created by Mateusz Mucha and Piotr Małek
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Sep 18, 2020
Golden rectangle calculator determines the missing side and area of a golden rectangle.
Golden rectangle, marked with lengths a, b, and a+b

The golden rectangle calculator will calculate the length of either side and the area of the golden rectangle, provided you give the other side. Before you use this calculator, you should understand what a golden rectangle is, how to calculate ratios in general and the formula for the golden ratio.

What is the golden rectangle

The golden rectangle is a rectangle whose sides are in the golden ratio, that is (a + b)/a = a/b, where a is the width and a + b is the length of the rectangle. The ratio calculator is an effective tool to assist in calculating ratios in general, while the golden ratio calculator will do the same as the golden rectangle calculator with the exception of finding the area of the rectangle.

Want to know how to use our golden rectangle calculator? Here are the steps:

  1. Enter the width a.
  2. Enter the length a + b or segment b
  3. Find the area a * (a + b)
  4. If you know the area, divide by the missing part to get the other part.
  5. Check your answer with the golden rectangle calculator.

An interesting aspect of the golden rectangle is that when the square section is removed, the remainder is another golden rectangle. Also, if you add another square to the rectangle with a side length of a+b, that is another golden rectangle. The golden rectangle calculator will verify this.

Mateusz Mucha and Piotr Małek
Golden rectangle, marked with lengths a, b, and a+b
a
in
b
in
a + b
in
Area
in²
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