Slope Percentage Calculator
Welcome to the slope percentage calculator, where you can learn all there is about expressing slopes as percentages. Be it for a math assignment or for understanding road signs; you're at the right place! In this article, we will discuss:
- How to calculate slope in percentage;
- Angle in degrees vs. percentage slope; and
- Determining slope percentage with the help of our tool.
💡 To learn about slope from a more theoretical point of view, in particular about the slope of a line in the Cartesian plane, visit our slope calculator.
How do I calculate slope percentage?
To find the slope percentage, follow these steps:
- Measure the rise (the vertical distance that the terrain rises or falls). Make this number negative if we're going downhill.
- Measure the run (the horizontal distance covered by the slope).
- Divide the rise by run.
- Multiply the result by 100 to turn it into a percentage.
In summary, the slope percentage formula reads:
slope percentage = rise / run × 100
🙋 To read more about the rise over run formula, visit our dedicated rise over run calculator.
Now, let's discuss how to convert between slopes expressed in degrees and percentages.
Converting slope percentage to degrees
To convert from degrees to slope percentage, use this formula:
slope percentage = tan(d) × 100
d is the slope in degrees. If your angle is given in radians, you must perform angle conversion first.
To go from slope percentage to degrees, apply this next formula:
angle = atan(s/100),
angle is in degrees,
s is the slope percentage, and
atan is the inverse tangent function. Go to our arcus tangent calculator to learn more.
How to use this slope percentage calculator?
There's nothing easier than using Omni's slope percentage calculator! Input your data (either both the rise and run or the angle in degrees) — and the slope percentage gets computed immediately!
Our tool can work in reverse as well! If you input the slope percentage, the angle in degrees will be calculated for you. And if you supply either the rise or the run, the remaining missing value will appear!
⚠️ Make sure that the angle in degrees you input is between -90° and 90°, excluding these two values! Note that the slope percentage tends to ±infinity as the angle approaches ±90°.
Can slope percentage be negative?
Yes, the slope percentage can be negative! A positive slope means the terrain rises, while a negative slope means it falls. The greater the absolute value of the slope percentage, the steeper the rise or fall is.
Can slope percentage be over 100%?
Yes! The slope percentage of 100% corresponds to the angle of 45°. Slopes above 100% exceed 45°, and so they are very steep indeed. For instance, the slope of 60° corresponds to the slope percentage of 173.2%. In fact, when the angle approaches 90°, the slope percentage goes to infinity!
How long is a ramp with rise 1 m and slope 5%?
The run of the ramp is 20 m. This is because of the slope percentage formula that reads
slope percentage = rise / run × 100.
Plugging in our data, we obtain
5 = 1 / run × 100, from which we easily find
run = 20, as claimed.
Is a rode with 5% slope steep?
Not really. A 5% slope means that the road rises 5 meters (or feet) over a run of 100 meters (or feet). This corresponds to the angle of less than 3 degrees above the horizontal. Whether or not you consider this steep really depends on your personal definition of steep!