How to Create a Wheelchair Ramp Using Right Angled Triangle Trigonometry


Wheelchair accessibility requires modifications to house and home. Steps and stairs pose a major obstacle to people confined to a wheelchair. Overcoming the obstacles calls for you to construct a ramp. Creating or designing the ramp means you need to evaluate the various dimensions of the structure and the needs of the person. Trigonometry offers simple ways to determine the length and width of the ramp, angle of incline, and the total area of landings.

Things You'll Need

  • Scientific calculator
  • Tape measure
  • Calculate the width needed for the ramp. The ramp needs to be as wide as the chair plus 12 to 24 inches on each side for elbow room.

  • Calculate the area for any intermediate landings that may be needed. For a standard intermediate landing, where a 90 degree or less turn occurs, 48 inches by 48 inches suffice. If greater than a 90-degree turn occurs, the area will be 48 inches by twice the width of the ramp.

  • Determine the area for the main landing. For doors or entryways, the landing should be 60 inches by 60 inches, or greater, for doors that swing outward. For doors that swing inward or slide, 48 inches by 48 inches should suffice. If the person has additional needs at the landing, such as setting down packages or picking up an item, increase the measurements by the area needed for the additional tasks.

  • Measure the height of main landing. Measure from the ground to the lip of the entryway. An entryway should not have more than a 1/2-inch lip when passing through, so the landing associated with the entryway should be flush. The measurement you get is your rise.

  • Calculate the length necessary for the ramp (slope). The maximum angle you should use is 4.76 degrees which is a 1:12 rise to slope ratio. A steeper angle than this becomes difficult to navigate. Depending upon the person's abilities, you may want to decrease the angle. Using a scientific calculator, find the SIN (the calculator will have a button saying "SIN" on it) of the angle you desire. The SIN of 4.76 is 0.08298.

  • Divide the SIN of your angle by the height needed. If the height measurement from step four is 36 inches of rise, divide the SIN by 36. The example results in 0.002305. Divide one by the result you get. For the example, divide 1 by 0.002305 which results in 433.84 inches which is the length of the slope necessary for a 4.76 angle at 36 inches of height. Divide that by 12 to translate it to feet (36.15 feet for the example).

  • Calculate the length you will need on the ground, which is the run for the ramp. Find the square of your measurement of the slope from Step 6 (i.e. 433.84 inches squared is 433.84 times 433.84 equaling 188,217.1456). Find the square for the measurement of the rise from Step 4 (per the example, 36 inches squared is 36 times 36 equaling 1,296).

  • Subtract the square of the rise (1.296) from the square of the slope (188,217.1456) and then find the square root (the button on the calculator that looks like a check mark that turns into a standard divide symbol) of that answer (188,217.1456 - 1,296 = 186,921.1456, square root of that answer is 432.34 inches or 36 feet) to determine your run. You now have the distance on the ground (run) that the ramp will cover, the distance of the slope, and the height.

  • Map out the layout for the ramp. Using the measurements for the landings, determine if you will need intermediate landings. The run will extend from the edge of the main landing to the edge of any intermediate landing, and then continue on from the other edge of that landing to the main lower landing. For example, if the overall measurement of the run is 36 feet and you have one landing that is 4 feet, measure from the edge of the main landing 12 feet (or your desired length), then 4 feet for the intermediate landing, and then 24 feet (36 minus the 12 feet of the first section) to see where the ramp will hit the ground.

Tips & Warnings

  • The calculations are complex. Using a calculator like the one in the Resources section allows you to enter just two of the calculations (height and the angle) and provides you with the rest of the measurements without complex math.

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