Finding the area of a square is an elementary geometry formula, with:

X2 = Y

...where X is the measure of one side of the square and Y is its area. It seems simple enough that you wouldn't need a special calculator, but this one also converts between various units of measuring length and area. Before we get into that part, however, we need to know what happens when you don't know the side measure. If you have other information on the square, there are a few other formulas that will work for other measurements:

•	X = diagonal measure - X^2 / 2
•	X = perimeter - X^2 / 16
•	X = the radius of the smallest circle you can draw outside the square (circumradius) - X^2 * 2
•	X = the radius of the largest circle you can draw inside the square (inradius) - X^2 * 4

Now, most things in nature don't happen to be perfectly symmetrical squares, so we also use the formula for finding the area of a rectangle.

X * Y = Z

...where X is the long side measure, Y is the short side measure, and Z is the area. However, you can adapt any rectangle into a square by finding the average between the two side measures. For instance, the area of a 2x8 rectangle is the same as the area of a 4x4 square.

Our calculator converts between standard units including the metric standard (meters, centimeters, and so on), and imperial units (feet, inches, yards, and so on). You can get an answer in square metric units, or hectares, acres, or even "soccer fields," for very large areas.

Hope you found this mini-refresher course in basic geometry useful.

Squares in Mathematics

The humble square has been the source of several mathematical mysteries almost as numerous as the circle. In the first place, 90-degree right angles and straight edges aren't found very often in nature, so it took a while to figure out how to build one.

The ancient Greek mathematician Euclid (300 B.C.) was the first to tackle an easy way to make a perfect square using only a compass and straight-edge, and furthermore able to find all four corners in just five lines.

Other geometric applications of squares proved not to be so easy to solve. "Squaring the circle" is an operation where you construct a circle which has the identical area of a given square.

It seems like a simple enough problem, as we know both how to find the area of both a circle and a square, and how to construct a circle or square for a given area. For years, mathematicians looked for a Euclid-based solution before the problem was finally proven to be unsolvable in 1882 by the Lindemann–Weierstrass theorem.