Stair Geometry

The 2R + T comfort formula behind modern stair codes predates any building code by more than two centuries. Francois Blondel, director of France's Royal Academy of Architecture, published the relationship in 1675 after studying how people actually walk: he found that a comfortable stride covers roughly 24 French inches on level ground, and that climbing trades horizontal stride for vertical lift at roughly a two-to-one rate. Doubling the riser height and adding the tread depth reproduces that natural stride length on a slope, which is why stairs built to the formula feel effortless while stairs that violate it -- too shallow or too steep for their proportions -- force an awkward shuffle or an exhausting high step.

Modern residential and commercial codes did not invent this relationship; they codified it, translating Blondel's comfort range into enforceable minimums and maximums for riser height and tread run, along with strict limits on how much those dimensions can vary from step to step within a single staircase.

A staircase can meet every riser and tread minimum in the code and still be dangerous if the steps aren't consistent with each other. A person's gait adapts to the first few steps of a flight and expects the rest to match; a single riser that's noticeably taller or shorter than its neighbors is a well-documented trip hazard because it breaks that learned rhythm exactly when a misstep is hardest to correct.

That's why the IRC and IBC regulate consistency within a flight as strictly as they regulate the absolute riser and tread numbers, typically limiting the variation between the largest and smallest riser (or tread) in a single staircase to a fraction of an inch -- a tolerance far tighter than the overall allowable range for riser height itself.