This article explains the method of calculation used to find the square of a number and the square root of a number. The explanation applies to calculating the length of a piece of lumber needed for a stair stringer as required in building stairs. However, the information is relevant anytime one needs to find the square or square root of a number.
How to square a number.
When you see an elevated "2"
(102)
at the end of a number it means that the number is to be multiplied by itself:
As an example:
In mathematical terms a number which is presented as 102 means that you are to multiply the number 10 by the number 10.
102 could also be written as 10 X 10
How to find the square root of a number.
When you see a square root symbol
(√)
it means what number when multiplied by itself would equal that number.
As an example:
√100 would be 10, because 10 x 10 equals 100.
If you were constructing a set of stairs, you would need to calcule the length of the piece of lumber necessary to make the stringers for that specific set of stairs.
The formula is:
Total Rise2 + Total Run2 = Length of Stringer2
The formula could also be written as:
(Total Rise X Total Rise) + (Total Run X Total Run) = Length of Stringer X Length of Stringer
Or, based on our specific example in:
"How To Build Stairs"
(106.75 X 106.75) + (140 X 140) = 30,995
Or
106.752 X 1402 = 30,995
To complete the stair stringer length calculation we need to know what number when multiplied by itself will equal 30,995.
The square root of 30,995 is 176.054
Note: Finding the square root of a number can be done manually. However, most calculators and spreadsheets have a square root calculation function! In Microsoft Excel the function is SQRT. If you go to a cell in an Excel spreadsheet and enter; =SQRT(30995) you will end up with a resultant of 176.054
This number is the length of the stringer in inches. Hence to make it into feet we divide the number by 12:
176.054 รท 12 = 14.67 feet
0.67 of a foot is 8 inches. This is determined by multiplying 12 (the number of inches in a foot) X 0.67 (the fraction amount of feet that we have from our calculation), which equals 8.