The **rectangle perimeter calculator** automatically gives values for any rectangle given the measurements **X** and **Y**, for the length of any two of its adjacent sides. It also gives the area, the diagonal length, the angle of the diagonal, and a circumcircle radius, all convertible in both metric and imperial units. Let's break this down in plain English:
**•** **X** and **Y:** The measurement along the "top" edge of the rectangle, and the measurement along one "side."
**•** **Area:** X * Y
**•** **Diagonal:** Any straight line drawn between two opposite corners of the rectangle. The hypotenuse of a right triangle taken from the rectangle.
**•** **Angle:** The number of degrees between two opposite diagonals of the rectangle.
**•** **Circumcircle:** The smallest possible circle that can be drawn whose perimeter touches all four corners of the rectangle. This answer is given as a radius, always of the value (diagonal / 2).
Of course, if both **X** and **Y** are the same, what you have is a perfect square, and the diagonal angle will always be 90 degrees.
If you try putting the angle as less than 91 degrees, the calculator will stop with an error message, because it is expecting a rectangle where one side is always longer than the other.

There's no mystery to rectangle calculation, most of it being based in elementary math:
**•** *Perimeter = (X * 2) + (Y * 2)*
**•** *Area = X * Y*
**•** *Diagonal = √((X ^ 2) + (Y ^ 2))*
**•** *Circumcircle radius = Diagonal / 2*
The angle part is the only tricky one, requiring we take the inverse of the standard trigonometric function tangent. Not exactly an equation that will come up in everyday life, but a standard poser on high school math exams.

**Rectangles** are the most basic shape introducing us to the concept of ratios, where two different values interact. But there is one ratio above all with the most interesting properties, the golden ratio, best expressed as:
*a | b = (a + b) | a*
**A** plus **B** is to **A** as **A** is to **B**. Values for golden rectangles are easily computed using the Fibonacci sequence: Take any two numbers, add them together, and then keep repeating this step with the last two numbers in the series:
**1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…**
The higher you get on this series, the closer you come to the true golden ratio, a number which, like Pi, is infinite and transient.
The curious thing about the golden ratio is that it shows up everywhere in nature, from the spiral of seashells to the spine placement on pine cones. Studies have shown that we find golden rectangles and other shapes using the golden ratio as most pleasing to the eye.