How to Calculate Percent Slope

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How do you calculate the slope percentage of a road or a ramp? What does "a 6 percent grade" mean?

Knowing the slope of a hill or a ramp can be very useful. The slope is the ratio between the change in elevation over the distance covered, also known as the rise over the run. In this article, you will see how to calculate the slope ratio of a road or a ramp.

When building roads, the slope is important because some vehicles cannot go up or down slopes that are too steep. Similarly, if you were making a wheelchair ramp, you would want to ensure that the slope of the ramp is manageable for the wheelchair user. To achieve either of these tasks, you'll need to know how to calculate the percentage slope for any ramp.

TL;DR (Too Long; Didn't Read)

Calculate the slope ratio using the formula: S = E/D (in words, slope ratio = elevation / distance). To get a percent slope, multiply the result by 100.

Slope Percentage Calculator: Elevation Versus Distance

To calculate the percent slope, or the slope ratio, you will need to know the change in elevation and the distance. This same approach can be used as a ramp slope calculator for any ramp with a consistent slope.

First, determine the change in elevation from the start to the finish of the slope and call this E for elevation. If you are determining the slope of a ramp, you can use a measuring tape. For determining the percent slope of a road, you can use a topographic map.

Second, determine the distance over which the change in elevation takes place and call this D for distance. Again, you can use a measuring tape for (small) ramps. For roads, you can use the scale on the map to figure out the distance.

With these two numbers, you can calculate the slope ratio using the following formula: S = E/D with S being the slope ratio. For example, if there were a 100 foot change in elevation over 1000 feet of road, you would have a slope ratio of 0.1.

From Slope Ratio to Slope Percentage

To obtain the percent slope, multiply the result from the calculation above by 100. In this example, the percent slope would be 0.1 × 100 = 10 percent. The percent slope would be 10 percent. You don't need to mention any units (such as "2 percent slope in feet"), because percentages are unit-less!

This same calculation can be used to determine the slope of any sloped construction, such as the pitch of a roof, the slope of a skateboarding ramp or the slope of a bridge.

Gradient, Percent or Degrees?

There are a number of different ways to express a slope, even though they all relate to the same measurement.

Slope gradients are shown as E:D, with E the elevation and D the distance. Both measurements should be in the same unit. In our example, the slope gradient would be 100:1000 or 1:10. This is read as a "one in 10 slope."

Slope percent is shown as a percentage. This is the example given in the previous section, and can be read as "a 10 percent slope" or "a 10 percent grade."

To calculate the slope in degrees, you will have to do a bit more of a calculation. From trigonometry, we know that the tangent of a given angle is the ratio of the opposite side (the elevation) and the adjacent side (the distance). The inverse tangent of the elevation divided by the distance will give you the angle in degrees: tan −1 (E / D). In our example, that gives us tan−1(100/1000) = 5.7 degrees slope.

References

About the Author

Valerie is a freelance science communicator, with a passion for all that is STEM. She has a Bachelor of Science in bio-engineering, a Master of Science in nanoscience and nanotechnology, and a PhD in Life Sciences - focusing on biophsyics and biomechanics. She writes often for her personal blog as well as for the blog of the Marie Curie Alumni Associaton. She currently works at Camps for Curious Minds at Pacific Science Center (Seattle) and has recently been involved in an art-science book project, for which she wrote compelling stories about inspirational scientists.

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