In mental terms, carpentry math is the hardest part of any rough framing carpenter's job. Many carpenter's never venture beyond simple addition and subtraction. Simply because they are intimidated by words, such as trigonometry, geometry, hypotenuse, or Pythagorean Theorem.
There are many different ways to apply every day math to these some times complex equations. You do not really need to know every aspect of these mathematical equations. The job can usually be accomplished with a simple pocket calculator,tape measure, and a little practice.
Do you need a quick answer to an addition or subtraction problem that has you stumped? Borrow your coworkers tape measure, then simply measure the two numbers together
One of the more common problems I have encountered over the years is determining correct wall height. This usually occurs when a two story open foyer is required. Here is the procedure I usually follow, add the two wall height's together, add the floor joist dimension, add the sub floor dimension, and subtract the wall plates thickness. This will give you the length of the studs. Here is what it looks like on the calculator. 97 1/8" + 97 1/8" = 194 1/4" + 9 1/4" = 203 1/2" + 3/4" = 204 1/4"  4 1/2" = 199 3/4".So we need to cut our studs at 199 3/4" or 16' 7 3/4".
One of the every day carpentry math problems encountered by carpenter's is the squaring up of walls or sill plates. When the object needing to be squared up is a rectangle it is a rather straight forward process of measuring diagonally until you come up with the same number from all four corners. We all know that in carpentry many times objects are shaped different than a simple rectangle. If it happens to be shaped like a "L" then you need a more powerful tool called the "Pythagorean Theorem".
This is nothing more than the old 6  8  10 rule which many of us use every day with out realizing it. You do not have to simply stick to 6  8  10, you can use any division or multiplication of this number. For example, 3 4  5 or 12  16  20 can also be used. You can also go from exact point to point for a very accurate 90 degree angle. This can also be accomplished with a regular pocket calculator. Check out the neat little calculator that I found the other day, go ahead play with it all you want.
Enter any numbers you like in the first two boxes and press solve for the hypotenuse.
Numbers should be entered as whole number and decimal points, for example. 119.25 = 119 1/4".
Many times the exact location of windows and doors are not clear on the blueprint. Let's say that you need to center a door in a hallway. I've found it easiest to find the center of the hallway, then divide the header size in half. Hold your tape measure on the center hallway mark and lay opening out from there.
Often you will be required to locate two or more evenly spaced windows in a single room or wall. The first step is to determine if the windows are centered in the room or from the outside corners. The trick to using carpentry math to locate multiple, evenly spaced, windows is to divide the space by one more number than you have windows. For example, 2 windows = divide by 3, 3 windows = divide by four, and so on.
Lets just say you have to put 5 window's in a 24' wall centered from the outside corners. Here are the steps I would take, divide 24' by 6. 24 divided by 6 = 4. The 4' measurement is to the center of the window, not the edge. Next measure in 4' from each corner and make a mark, then measure what you have between these two marks. It should be 16'. If this is so then your carpentry math is correct and you can now lay out the rest of the windows on 4' centers. Remember these lay out marks are to the center of windows, so mark headers and king studs accordingly.
This can also be accomplished with a regular calculator. Below there is a table for quick reference.
1/8"  1/4"  3/8"  1/2"  5/8"  3/4"  7/8" 
.125  .25  .375  .5  .625  .75  .875 
I hope this web page has helped improve your carpentry math skills. Bookmark this site and come back often, new information is added regularly.
