What is the approximate stringer length of a custom staircase with a rise of 12' and a run of 16'?

To find the approximate stringer length of a custom staircase, you can use the Pythagorean theorem, which applies to right triangles. In this scenario, the rise and the run of the staircase represent the two legs of a right triangle, where the rise measures 12 feet and the run measures 16 feet.

According to the theorem, the length of the stringer (the hypotenuse of the triangle) can be calculated using the formula:

[ \text{Stringer length} = \sqrt{(\text{rise})^2 + (\text{run})^2} ]

Substituting the given values:

[ \text{Stringer length} = \sqrt{(12)^2 + (16)^2} ]

[ = \sqrt{144 + 256} ]

[ = \sqrt{400} ]

[ = 20 \text{ feet} ]

Thus, the stringer length of the staircase is approximately 20 feet.

This calculation is vital for determining the structural integrity and spacing of the staircase, ensuring it meets safety and design codes. Understanding how to accurately calculate the stringer length is essential for any cabinet and millwork or finish carpentry projects involving staircases.