Before you can put a railing on stairs, you have to calculate the correct railing angle. Railings make stairs safer and can be ornamental, but their angle must match the angle of the stairs. You can calculate the angle required for railings by measuring the stairs and applying trigonometric functions to find the corresponding angle. Knowing the angle lets you make the angled cuts for the banister and supports accurately so the different parts of the railing join tightly and offer firm support.
Place the framing square vertically on one step and measure the height of the step from the step surface to the top of the step above. If the step has a bull-nose, or bit that sticks out, measure to the top of the bull-nose. Write down the exact value, which should be about 7 to 8 inches.
Measure the depth of the step from the edge of the step or the edge of the bull-nose to the riser at the back of the step. If there is a bull-nose, measure the length it sticks out and subtract it from the depth of the step to get the value for calculating the run of the staircase. Write down the exact value of the run, which should be around 10 to 11 inches on a standard household staircase.
Measure the heights, depths and runs for each step on the staircase and note down the exact values. Add the heights and runs for all the stairs to get the total rise and run for the staircase, and write down the totals.
Use the measuring tape to find the length of the staircase. Stretch the measuring tape from the bottom of the staircase to the top, securing the end of the tape measure to the edge of the top stair with adhesive tape. Measure along the edges of the stairs to the floor at the bottom. Write down the exact value for the total length of the staircase.
Set your calculator to calculate trigonometric functions in degrees. Divide the total rise by the total run of the staircase. Then calculate the inverse tangent of the result. The answer is the angle the staircase makes at the bottom, and it will be the angle at which your railing rises.
Check your calculations by dividing the total rise of the staircase by the total length. Then calculate the inverse sine of the result. The answer should be the same angle as you calculated using the inverse tangent. Check your measurements and calculations if there is a substantial difference. The angle should be between 20 and 38 degrees.