How To Calculate Length of Stair Stringer - Easy To Understand Construction Tips

The video goes over the process of using the Pythagorean theorem to calculate the length of the stair stringer. Once you have obtained the lengths of the treads and the risers, you can use the Pythagorean theorem to calculate the length of the stair stringer, so that you can purchase the correct lumber lengths.

The Pythagorean theorem is a mathematical formula that relates the lengths of the sides of a right triangle. The formula is a² + b² = c², where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse. In the case of a stair stringer, the hypotenuse is the length of the stringer, and the legs are the lengths of the treads and the risers.

To calculate the length of a stair stringer, you first need to obtain the lengths of the treads and the risers. The lengths of the treads can be obtained by measuring the horizontal distance between the faces of two adjacent risers. The lengths of the risers can be obtained by measuring the vertical distance between the top of one tread and the top of the next tread.

Once you have obtained the lengths of the treads and the risers, you can use the Pythagorean theorem to calculate the length of the stair stringer. To do this, you simply plug the lengths of the treads and the risers into the formula and solve for c.

For example, suppose that the lengths of the treads are 12 inches and the lengths of the risers are 7 inches. Then the length of the stair stringer can be calculated as follows:

a² + b² = c²
12² + 7² = c²
144 + 49 = c²
193 = c²
c = √193
c ≈ 13.9 inches

Therefore, the length of the stair stringer is approximately 13.9 inches, mulitplied times the number of steps plus one. If I had 6 steps, then I would multiply 7 times 13.9 to get, 97.3 inches. Suggesting that I would need an 8 foot 2 inch or longer piece of lumber for my stair stringer. You can multiply by 6 steps, but you will need to add a few inches.

Back To Basic Stair Building

Here's an easier method, but it won't provide an exact length, if you have a situation like this.

Then you can establisth the stairway starting point.

And measure the distance to calculate rough length of stringer. Just add a few inches or even a little more if you can. For example, if my mesurement is 92 inches, then I will need an 8 foot long piece of lumber, but it might be better to get a 10 foot long piece. Then layout my pattern to verify my measurement to purchase the other stringers.