How to Calculate a Stair Stringer

Attach a plumb line at the top front of the joist where the staircase will begin. Hammer a nail to the joist, then wrap the string around the nail and allow the plumb line to hang straight down. This is your rise. You will use this to calculate the vertical height of each stair.

Envision where the steps will end. Just beyond this point, insert a wooden stake into the ground, keeping the stake in line with the plumb line. Wrap a length of string around the stake several times, and attach the string level to the string. Stretch the other end of the string back toward the plumb line.

Insert a new stake just past the plumb line. Determine if the string is level, then wrap it around this stake. Double check that the line remains level. The distance from the plumb line to the first stake represents the run, or length of the staircase.

Choose a stair height to begin your calculations. Most steps are 6 1/2 to 6 3/4 inches tall. It is important to keep all steps the same height and depth to prevent tripping hazards.

Divide the overall rise by the desired height of each step. The result will be the number of steps you need to create. For example, if you have a rise of 60 inches and a desired stair height of 6 1/2 inches, the result is 9.23 steps. Because this is not a whole number, adjust the calculations until the result is a whole number. In this case, reducing the rise to 6 inches would yield 10 steps.

Determine the length of each tread by dividing the total staircase run by the desired horizontal depth of each tread. A good place to start is a desired tread of 11 inches. For example, a run of 45 inches divided by a desired tread of 11 inches equals 4.09. That means there will be four steps, but the remaining .09 (divided by four) is too small to be used for overhang on each step. You then have two choices. Use no overhang and reduce the run to 44 inches. Or, you can increase the staircase length to 48 inches, which allows about an inch of overhang.

Find the ratio of rise to run for each step once all your calculations are done. The ideal rise to run ratio can be found by adding the two measurements together. The ideal calculation is Rise + Run = 17 to 18 inches. This allows the staircase to be at an angle that is neither too shallow, nor too steep. If the numbers do not add up in this range, you need to make adjustments to the tread depth first. The total height of the staircase is often not able to be changed. If altering the tread size does not work, you may need to go back to your original rise calculations and add or subtract another step while increasing or decreasing the rise accordingly.