How to Square Your Work
by Damien Andrews
One of the most common (and worst) problems doityourselfers run into is a finished job that is not properly squared. For a job to be squared, it does not have to be a square – it merely needs to have right angles, which are angles at 90°. A square and a rectangle both have 90° corners.
Many tasks taken on by doityourselfers require proper squaring of the job. Examples would include erecting the frame for a small building; pouring a concrete pad for a barbecue grill; and constructing the frame for a table. In some jobs, if an error is made in the squaring, everything that follows will be wrong – or at the very best require extensive parts and labor to correct. If you pour your new workshop's concrete pad and it's out of square, you'll encounter some serious problem when it's time to erect and install the wall frames – and so forth.
To properly square a job, you're going to want a small calculator that will compute the square of a number, or access to a computer with a numbers program that will compute the square of a number. If you're a serious doityourselfer, you might want to look into one of the less expensive, handheld contractor's calculators that are available. While I avoid mentioning specific products in these articles, in this case I'll say that I very much like the InchMate®+ by Sonin®. It costs less than $20, and does everything needed for common jobs. Some handheld contractor's calculators cost in the hundreds, and they are excellent tools to have, but largely unnecessary for even the most advanced doityourselfers.
Referring to the artwork below, we're after a rectangle that matches Diagram 1 – NOT Diagram 2. Diagram 2 is a parallelogram or quadrilateral. The lengths of lines A and C are equal, as are the lengths of lines B and D – but the shape is not squared. This unsquared, sometimes referred to as skewed, shape will not work well at all. So let's look at how to get the look of Diagram 1.
You'll always know the measurements of your work's sides, which is all we'll need to compute the hypotenuse. It's the hypotenuse that we'll use when measuring and marking to ensure that we end up with perfectly squared work. The formula for computing a hypotenuse is:
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
Or using our Diagram 1
A² + D² = Hypotenuse²
To solve the problem to its completion:
Hypotenuse = √A² + D² (the square root of A² + D²)
Let's plug in some real numbers and work stepbystep to further clarify the formula:
Side A = 10'
Side D = 20'
Side A² (10' x 10') = 100'
Side D² (20' x 20') = 400'
A² + D² = 500'
The square root of 500' is 22.36'
Ergo, the hypotenuse of a rectangle with one leg of 10' and the other leg of 20' is 22.36'.
To determine what .36 of a foot is, multiply .36x12, which will give you: 4.32". Now we know that the hypotenuse is 22' 4.32". To determine what .32 of an inch is, refer to the following chart, which will get you very close – close enough for all but the very finest of work tolerances:
FRACTION 
DECIMAL 
1/16" 
.0625 
3/16" 
.1875 
5/16" 
.3125 
7/16" 
.4375 
9/16" 
.5625 
11/16 
.6875 
15/16" 
.9375 


1/8" 
.1250 
3/8" 
.375 
5/8" 
.625 
7/8" 
.875 


¼" 
.25 
½" 
.5 
¾" 
.75 
As we can see in the provided chart, .32 is almost a perfect 5/16". So now we know to measure the hypotenuse at: 22' 45/16". (By the way, that handheld contractor's calculator I mentioned above will translate decimals into fractions for you – down to a 64 th of an inch.)
Now let's create our perfect 10' x 20' rectangle. Put a stake in the ground at point X and measure the 10' east to where line A meets line D. Drive another stake in at this point. Attach one end of your measuring tape to this point and run it out to point Y. Now go back to point X and run another measuring tape at a diagonal to point Y. Shift the two tape measures as necessary until the diagonal measuring tape reads 22' 415/16" and the straight measuring tape reads 20'. Put your next stake there. You now have three stakes in the ground. Now, place one measuring tape at point X and open it north 20'. Place the other measuring tape at point Y and open it 10'. Where the two intersect is where you'll want to place your fourth, and final, stake.
Remember the Carpenter's Mantra: Measure twice, cut once! In this instance, that means to go around and double check all your measurements – including the hypotenuses running in both diagonals. If you need to slightly shift your stakes to get them perfect, do so now. It really is worth the extra effort.
Pro Tip: 5/8" rebar cut to 24" and 36" lengths makes great stakes for outdoor ground projects. Be sure to drive your stakes in straight so that the top of the stake represents the same measurement as where the stake is placed. If the stake comes up at an angle, your measurements will be off whenever you use the top of the stake as a starting point. You can reuse these stakes many, many times – even after having driven them into hard ground with a small (35#) sledge hammer.
