This equation computes the length of the side of a square whose boundary is the same length as a circle of radius r.

In other words, if you had a string and it was just long enough to wrap around a circle of radius r, this equation computes the length of the side of a square around which the same string just reaches.

Examples

Example 1: If you enter a radius of 3.5 meters, the circumference of the circle of radius 3.5 meters is equal to the distance around a square whose side is close to 5.5 meters.

Example 2: If you had a flexible circle of radius 1.114 units, you could make it fit pretty snuggle around a square of side 1.75 of the same units.  the two red boundaries in the picture are equivalent in length.

Application

If you had a flexible pipe with a radius of r and you wish to form-fit the pipe tightly over a square device, how large would the square have to be on a side for the flexible pipe to fit very snuggle.