Q: The stair layout method described in Training the Trades (Apr/17) was great, but what do you do when the rise turns out to be an odd fraction?

A: Greg Burnet, author of Training the Trades and a remodeling contractor from Chicago, Ill., responds: We used a fairly simple example in the column on purpose, but in reality, the rise calculation rarely works out to a nice, even fraction. For more complex situations, I break out my Construction Master calculator. I go through the same initial steps as described in the article, but then double-check my calculations by multiplying the rise dimension that the calculator arrived at by the number of rises.

This figure hardly ever exactly matches the actual overall rise that I started with. Why? Because the Imperial measurement system that we use in this country is based on units of sixteenths and thirty-seconds and their multiples, and quite often these fractions are not equally divisible by what are essentially odd numbers. As a result, the calculator rounds up or down slightly, providing an approximate rise. The difference is then averaged between all the rises.

In some cases, this “close enough” method may be perfectly acceptable, but if I am doing fine finish work on the stairs, those differences may compound and require me to custom-cut all the finish pieces. Instead, I prefer to go a step further in the calculations.

So let’s say that the overall rise is 30 11/16 inches and I have four rises. Turning to the construction calculator, I enter the overall rise measurement and divide it by the number of rises (see calculation sequence, below left). I enter the result (7.671875) as “Rise,” and the Run (10), and then press the “Diagonal” key. This number (a hair less than 12 5/8 inches) is the hypotenuse of each tread-riser combination. With the number still displayed, I press the “+” key, then the “=” key, and so on, to calculate the number for each diagonal tread-riser location: 12 5/8 inches, 25 3/16 inches, 37 13/16 inches.

The calculator stores the leftover tiny fraction and rounds up or down accordingly. I have my calculator set to 1/16 inch, so these numbers are all rounded to the nearest sixteenth. This method works because it averages the weird little fractions to the closest sixteenth without creating accumulating errors. I write down these numbers as “Unit Diagonals.”

After setting up the square with gauges at the rise and run locations, I place the square against the stringer stock and mark the heel (the intersection of the tongue and body). I adjust a combination square to the heel mark and use it to scribe a line along the length of the board. Then I hook my tape measure on what will be the lower portion of the stringer and make tick marks at the Unit Diagonal measurements along this line. To lay out the steps, I slide the square along the edge of the stock until the heel intersects each tick mark, and then I strike the tread and riser lines at each location. The layout now should accurately reflect the exact overall rise of the stair, with each rise being equal.