Determining the vertical height (rise) and horizontal depth (run) of individual steps is fundamental to staircase design and construction. Rise refers to the vertical distance between the top of one tread and the top of the next, while run denotes the horizontal distance from the front of one tread to the front of the next. For example, a staircase with a total height of 84 inches and a desired step height of 7 inches would require 12 steps. If the available horizontal space allows for a 10-inch tread depth, each step would have a 10-inch run.
Proper dimensional calculations ensure safety, comfort, and adherence to building codes. Consistent and appropriate step dimensions minimize the risk of trips and falls, contributing to a safer environment for users. Furthermore, compliance with established regulations is crucial for obtaining necessary building permits and ensuring structural integrity. Historically, formulas and guidelines have evolved over time to optimize staircase design for human biomechanics and accessibility.