Changes in Level and Floor Surfaces (2010 ADA Standards 302, 303)
Three thresholds, and the last is a cliff. Up to 1/4 in a change may be VERTICAL -- a square edge, no transition. From 1/4 to 1/2 in it must be BEVELED at 1:2 or flatter, meaning the run has to be at least twice the rise, so a strip cut at 1:1 looks beveled and is not. Over 1/2 in it becomes a RAMP under 405: a 5/8 in change needs 7.5 in of run at 1:12 against the 1 in a bevel would have taken, plus landings, edge protection, and handrails. One sixteenth of an inch is the difference, which is why grinding the change down to 1/2 in almost always beats ramping it.
Formula and source
change in level <= 1/4 in may be vertical; > 1/4 in and <= 1/2 in must be beveled at a slope no steeper than 1:2, so the required run = 2 x the rise; > 1/2 in must be ramped under 405 or 406, so the run = rise x the ramp run per rise (12 for 1:12). Carpet pile <= 1/2 in. Openings must not pass a sphere over 1/2 in, and elongated openings run perpendicular to the dominant direction of travel.
2010 ADA Standards for Accessible Design, 302.2, 302.3, 303.2, 303.3, and 303.4. A US federal standard in the public domain, quoted directly.
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