Wheelchair Ramp: Which Constraint Actually Binds?
A contractor must build a wheelchair ramp to a door whose threshold is 27 inches above the sidewalk. The building code requires a slope no steeper than 1:12 - one inch of rise for every 12 inches of horizontal run - and requires a flat landing 5 feet long, measured horizontally, at the top of the ramp directly in front of the door. The only available straight run is 28 feet, measured horizontally from the base of the ramp to the wall containing the door. The ramp is a straight incline from the sidewalk up to the landing, and the landing sits at threshold height. All measurements are in inches unless stated. The contractor wants to know whether a compliant ramp fits, and if not, exactly which requirement is the obstacle.
1. What horizontal run does the code require for the ramp alone, and what total horizontal distance is needed including the landing? Compare with the 28 feet available.
Read the worked answer
Ramp run required: 27 in of rise × 12 in of run per inch of rise = 324 in = 27 ft.
Plus the landing: 27 ft + 5 ft = 32 ft total horizontal distance.
Available: 28 ft = 336 in.
Shortfall: 32 − 28 = 4 ft (48 in). A single straight compliant ramp with the required landing does not fit in the available space.
Sanity check with inches throughout: 336 in available − 60 in landing = 276 in of usable run; 276 ÷ 12 = 23 in of rise achievable, versus the 27 in needed.
2. If the contractor keeps the 5-foot landing, what is the highest threshold the straight run could serve at code slope? For that compliant design, how long is the sloped ramp surface?
Read the worked answer
Usable run for the incline: 28 ft − 5 ft = 23 ft = 276 in.
Maximum rise at 1:12: 276 ÷ 12 = 23 in. So the highest threshold this layout can serve is 23 inches - 4 inches short of the 27-inch door.
Sloped surface length (Pythagorean theorem): L = √(276² + 23²) = √(76,176 + 529) = √76,705 ≈ 276.96 in ≈ 23.08 ft.
The surface is only about an inch longer than the horizontal run because the slope is gentle - the 1:12 ratio makes the hypotenuse nearly equal to the run. Do not report 23 ft as the ramp length; the ramp board must cover 23.08 ft.
3. The contractor proposes skipping the landing and running the ramp the full 28 feet to gain height for the 27-inch threshold. Check the slope numerically, then explain whether this solves the problem.
Read the worked answer
Slope check: rise 27 in over run 336 in. Run per inch of rise = 336 ÷ 27 ≈ 12.44 in.
The code requires at least 12 in of run per inch of rise; 12.44 > 12, so the slope is gentler than the maximum and is compliant. Rise-to-run = 27:336 = 1:12.44.
But this does not solve the problem. The 28-foot run was measured to the wall, so using all of it leaves zero horizontal space for the required 5-foot landing. The design would violate the landing requirement - a safety rule, not a geometric one.
The judgment: the binding constraint here is the landing length, not the slope. The slope would pass; the flat approach would not. Valid fixes are a switchback (two shorter runs with a mid landing), relocating the door, or lowering the threshold by 4 inches - each of which changes the geometry rather than the arithmetic.