How to find the angle of a ramp

Designed to assist you in finding the access solution that will best suit your needs.

Finding the right ramp for your application can seem like a challenging task, however the EZ-ACCESS Incline Calculator can help. When you follow the few simple steps to use the tool, it will determine the ramp length that you need based on your rise and incline requirements.

Once the Calculator has provided you with the optimal ramp length that you need, it will recommend products that are available in that specific length.

Ramp Calculation Chart

How to find the angle of a ramp
This ramp calculation chart will help you figure out how long your Roll-A-Ramp should be.
How long of a ramp should I buy?

Generally Recommended Slope Angles:

4.8-degree: This is Americans With Disabilities Act compliant – click here for more information about Roll-A-Ramp and ADA

7-degree: Manual wheelchair users who are independent or who have an attendant with limited strength

10-degree: Manual wheelchairs with a reasonably strong attendant

12-degree: Power wheelchairs or scooters and manual chairs with a strong attendant

15-degree: Restricted space, unoccupied loading/unloading

How to find the angle of a ramp
Determining the length of a ramp is not complicated

Determining Ramp Length:
Measure total rise (how many inches from lower level to upper level) and divide by the slope.

4.8-degree: Rise distance divided by 1

7-degree: Rise distance divided by 1.5

10-degree: Rise distance divided by 2

12-degree: Rise distance divided by 2.4

15-degree: Rise distance divided by 3

Example: For a desired slope of 7 degrees with a rise of 12″ (1 foot), 12/1.5 = 8 foot ramp

Solving problems using trigonometry - slope angle

In this class of problems, we are given a slope or ramp with some dimensions known, and we are asked to find the angle of the slope or ramp.

Problem:

A ramp has been built to make a stage wheelchair accessible. The building inspector needs to find the angle of the ramp to see if it meets regulations. He has no instrument for measuring angles. With a tape measure, he sees the stage is 4t high and the distance along the ramp is 28ft.

Step 1. Draw a diagram

Include all the information given and label the measure we are asked to find as x. Draw it as close to scale as you can.

How to find the angle of a ramp

Step 2. Find right triangles

We can assume the side of the stage is vertical and makes a right angle at the floor (point C). So the ramp itself is a right triangle (ABC).

Step 3. Choose a tool Right Triangle Toolbox Reviewing what we are given and what we need: We are asked to find x, the angle at which the ramp goes up to the stage. We are given the hypotenuse (AB) and the side opposite the angle Looking at our toolbox, we are looking for a function that involves an angle, its opposite side and the hypotenuse. We see that the sin function meets our needs: where O = the side Opposite the angle, H is the Hypotenuse.

Step 4. Solve the equation

Inserting the values given and the unknown x: Using a calculator, divide 4 by 28: What angle has 0.1429 as its sine? For this we use the inverse function arcSine. It tells us what angle has a given sine.

Using a calculator* again, we find that arcSin(0.1429) is 8.22°, so

x = 8.22°

* Note: On calculators and spreadsheets, arcSin is sometimes called asin or sin-1.

Step 5. Is it reasonable?

We see from our calculation that the ramp angle is somewhere around 9°. Looking at our diagram we see this looks about right.
If you get a very different answer, the most common error is not setting the calculator to work in degrees or radians as needed.

Try it yourself

Repeat this problem with a stage height of 8ft. The ramp angle should come out to about 16.6°.

See it in reverse

See this example where the angle and stage height are known but the ramp length is not.

Other trigonometry topics

Angles

  • Angle definition, properties of angles
  • Standard position on an angle
  • Initial side of an angle
  • Terminal side of an angle
  • Quadrantal angles
  • Coterminal angles
  • Reference angle

Trigonometric functions

  • Introduction to the six trig functions
  • Functions of large and negative angles
  • Inverse trig functions
  • SOH CAH TOA memory aid

  • Sine function (sin) in right triangles
  • Inverse sine function (arcsin)
  • Graphing the sine function
  • Sine waves

  • Cosine function (cos) in right triangles
  • Inverse cosine function (arccos)
  • Graphing the cosine function

  • Tangent function (tan) in right triangles
  • Inverse tangent function (arctan)
  • Graphing the tangent function

  • Cotangent function cot (in right triangles)
  • Secant function sec (in right triangles)
  • Cosecant function csc (in right triangles)

Solving trigonometry problems

  • The general approach
  • Finding slant distance along a slope or ramp
  • Finding the angle of a slope or ramp

Calculus

  • Derivatives of trigonometric functions

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What is the angle of a ramp?

The commercial and public facility standard for slope is 1:12 (in inches) or about 5 degrees of incline. For those building ramps at home, the ratio can be as steep as 3:12 or almost 15 degrees. This is useful is space is really limited, however it can be difficult for motorized wheelchairs and powered scooters.

What is the formula for ramp?

Slope expressed as a percentage = (h/d) x 100 An existing ramp of 1 meter in height with a horizontal distance of 10 meters, will have a slope of 10%.

What does 1/14 mean for a ramp?

Calculating The Ramp's Slope 1, the gradient of wheelchair ramps with lengths of over 1,900 milimetres should not exceed 1:14 and should not be less than 1:10. This slope ratio indicates that for every 14 metres across the length of the ramp, the slope height increases or decreases by 1 metre.

What is a 1/20 slope for a ramp?

For the parts of an accessible route that aren't a ramp, the maximum running slope allowed is 1:20. That means for every inch of height change there must be at least 20 inches of route run. The distance from the bottom edge of the level to the surface should be no more than 1.2 inches (1.2:24 = 1:20).