# Pythagorean Theorem For Stair Building The Pythagorean Theorem: The sum of the areas of the two squares on the legs (A and B) equals the area of the square on the hypotenuse (C). The theorem is as follows:

In any right triangles, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

The square on the hypotenuse is equal to the sum of the squares of the other two sides.

If we let C be the length of the hypotenuse and A and B, the lengths of the other two sides, the theorem can be expressed as the equation.

A multiplied times A + B multiplied times B = C multiplied times C

Example: The stair riser height of A is 7 inches and the stair tread length is 10 inches.

7 x 7 = 49
10 x 10 = 100

Next Step 49 + 100 = 149

Next Step You will need to find the square root of 149.

On your calculator it will be a symbol that looks like this: Next Step Enter 149 into the calculator and press the square root symbol and the answer should be 12.20655

C would equal 12 and 1/4 inches. Now just multiply 12.2 times the number of steps or treads to get the length of the stair stringer. This is helpful when figuring out your stringer lengths, before purchasing them.

Using A Calculator To Figure Stair Risers