For a main stairway, how many risers would be needed if the total vertical distance is 8'-11" and the riser height must be less than 7 1/2"?

To determine the number of risers needed for a main stairway with a total vertical distance of 8'-11" and a maximum riser height of less than 7 1/2", it’s essential to convert the vertical distance into inches for easier calculations. The height of 8 feet 11 inches converts to 107 inches (since 8 feet is 96 inches and 11 inches adds 11 more).

Next, by dividing the total height of 107 inches by the maximum riser height of 7.5 inches, we calculate how many risers are necessary:

107 inches ÷ 7.5 inches ≈ 14.27.

Since risers must be whole numbers, we round up to ensure the entire height is covered, resulting in a need for 15 risers. This approach reflects the rule that risers should never exceed a maximum height for safety and comfort, thus confirming that using 15 risers will make the individual riser height slightly less than the maximum allowed when calculating the total height.

This method of calculating risers is fundamental in carpentry, ensuring not only compliance with building codes but also providing safe and comfortable stairway designs.