Ramp Calculator

A ramp is a right triangle in elevation, so its three geometric outputs follow from the rise and the chosen slope ratio. The horizontal run equals the rise multiplied by the ratio denominator, the sloped surface length is the hypotenuse given by the square root of rise squared plus run squared, and the inclination is the arctangent of rise divided by run. At the 1 in 12 ratio that anchors accessible design in the United States, the slope is 8.33 percent and the angle is 4.76 degrees. Gentler ratios of 1 in 16 and 1 in 20 give 6.25 and 5.0 percent, and a surface flatter than 1 in 20 is treated as a sloped walk rather than a ramp. Geometry alone does not produce a compliant ramp. The 2010 ADA Standards for Accessible Design cap running slope at 1 in 12 and cross slope at 1 in 48, require a minimum 36 inch clear width between handrails, and limit any single ramp run to 30 inches of rise before a level landing is required. Landings must be at least 60 inches long and no narrower than the ramp, and a landing where the ramp changes direction must be at least 60 by 60 inches, and handrails are required on both sides where the rise exceeds 6 inches. Alterations to existing buildings permit steeper exceptions, up to 1 in 10 for a rise under 6 inches and 1 in 8 under 3 inches, but these are relief provisions rather than design targets, since steep ramps are hard to ascend independently and dangerous when wet or iced.

The 1 in 12 figure is not arbitrary; it came out of empirical research on manual wheelchair use at the University of Illinois, where Timothy Nugent built a postwar rehabilitation and disabled-student program and studied what gradients users could actually negotiate without assistance. That work underpinned the first American national accessibility standard, ANSI A117.1, issued in 1961 under the title covering the making of buildings and facilities accessible to and usable by the physically handicapped. The standard was voluntary, so uptake was slow and uneven. Legislation supplied the enforcement. The Architectural Barriers Act of 1968 required federally funded buildings to be accessible, and Section 504 of the Rehabilitation Act of 1973 extended obligations to recipients of federal funds. The Americans with Disabilities Act, signed on July 26, 1990, generalized the requirement to most public accommodations and commercial facilities, and the Access Board issued the ADA Accessibility Guidelines in 1991 to give it technical content. Those guidelines were revised and adopted by the Department of Justice as the 2010 ADA Standards for Accessible Design, which became the compliance benchmark on March 15, 2012, and remain the source of the slope, width, landing, and handrail values used here. Model building codes and the current ANSI and ICC A117.1 standard were harmonized with these provisions, though individual jurisdictions can and do impose stricter local limits.