On a a construction site, we often encounter the same problem: a step of a few centimeters to overcome, a height difference to make up in a garage, or an access point to make compliant for a wheelchair. What length of ramp should be planned for a given slope in degrees? The answer lies in a simple trigonometric formula, but one must first distinguish what is actually being measured (the horizontal distance, the inclined length, the height) and not confuse degrees with percentage.
Degrees, slope percentage, and tangent: three concepts not to mix up
The most common mistake on site is treating degrees and percentage as synonyms. A slope of 10% does not correspond to an angle of 10 degrees. The relationship is based on the tangent: slope percentage = tangent of the angle multiplied by 100. Conversely, to find the angle from a percentage, we use the arctangent.
You may also like : How to calculate the ideal amount of fries per person for your meals
In practical terms, an angle of 5 degrees gives a slope of about 8.7%. An angle of 10 degrees rises to about 17.6%. Confusing the two units can lead to underestimating or overestimating the ramp by several tens of centimeters.
For those who prefer to check their conversions without using a scientific calculator, one can rely on a slope table in degrees on Une Autre Maison that automates the conversion from angle to ramp length.
Recommended read : How to Easily Find the New Fanstream Address in 2024?
Calculating ramp length from an angle in degrees
We have a height difference to overcome (the height) and a desired angle (in degrees). What we are looking for is the actual length of the inclined surface or the horizontal distance on the ground. The two are not identical, and this is a point that many guides overlook.
Horizontal distance and inclined length: two distinct measurements
The horizontal distance corresponds to the ground projection of the ramp. This is what we use in regulatory formulas (height divided by slope percentage). The inclined length, on the other hand, represents the actual surface on which one rolls or walks.
To transition from one to the other, we apply the Pythagorean theorem: inclined length squared = horizontal distance squared + height squared. If we know the angle, we can also directly use the sine and cosine.
- Horizontal distance = height / tangent of the angle. This is the space needed on the ground.
- Inclined length = height / sine of the angle. This is the length of material (board, metal ramp) to be planned.
- If starting from the slope percentage rather than the angle: horizontal distance = height / (percentage / 100).
Concrete example with a common step height
Let’s take a step of 15 cm to overcome. We aim for an angle of 5 degrees (which gives a slope of about 8.7%, compatible with accessibility requirements over a short distance).
Horizontal distance: 0.15 / tangent(5°) = 0.15 / 0.0875 = about 1.71 m. Inclined length: 0.15 / sine(5°) = 0.15 / 0.0872 = about 1.72 m. On a gentle slope, the difference between the two values remains minimal, but it widens as soon as we exceed 10 degrees.
Beyond 8 degrees, the difference between horizontal projection and actual length becomes significant, and it is essential to order the inclined length if purchasing a prefabricated ramp.
Regulatory slopes for accessibility for people with reduced mobility and impact on length
When working on access for people with reduced mobility, the slope is not arbitrary. The most common references in accessibility set 5% as the reference slope, with tolerances of 8% over 2 m and 10% over 0.5 m. These thresholds directly condition the necessary ramp length.
To translate these percentages into degrees: 5% corresponds to about 2.86 degrees, 8% to about 4.57 degrees, and 10% to about 5.71 degrees. We see that the allowed ranges remain at very low angles, which explains why compliant PMR ramps are often longer than expected.
Rest areas and turns in the total calculation
A straight ramp of several meters is not always feasible. When space is limited, we incorporate rest areas or turns (at 90° or in a U-turn). Each landing adds a flat area of at least 1.50 m in diameter to allow for wheelchair maneuvers.
The calculation of the total length then changes: we add the inclined sections and the intermediate landings. In a U-turn configuration, the developed length can double compared to a straight ramp, even for the same height difference. Returns on this point vary depending on the site configuration, but planning at least 30% additional length per turn is a reasonable field estimate.
Common errors that distort slope calculation in degrees
We have seen the confusion between degrees and percentage. Other traps frequently arise on construction sites and in quotes.
- Measuring the height from the wrong point: the height difference is taken between the finished floor below and the finished floor above, not between the raw slab and the door threshold.
- Forgetting the thickness of the ramp itself: a metal ramp a few centimeters thick adds height at the base of the ramp if the ground is not flush.
- Rounding the tangent loosely: for small angles, a deviation of 0.5 degrees can change the length by several tens of centimeters, especially when the height to be overcome exceeds 20 cm.
- Neglecting the non-slip surface: it does not lengthen the ramp, but a slippery surface practically requires reducing the slope, thus increasing the length.
Checking the actual height to be overcome twice before pulling out the calculator remains the most useful advice. A difference of 2 cm in height translates to 20 to 40 cm of additional ramp on a 5% slope.
The calculation of ramp length is not complex once one masters the distinction between angle in degrees and slope percentage. The tangent links the two, and the Pythagorean theorem wraps up the calculation to obtain the actual inclined length. In an accessibility project, the regulatory thresholds (5%, 8%, 10%) set the framework, but it is the precise measurement of the height difference on site that determines everything else.