We must remember that this is not the proper way to do so and it is not the method we learned in algebra class. The slope angle exactly equals what we previously calculated because instead of using the slope length as the run, we used it to calculate the true horizontal distance.Ĭalculating Grade By Using Slope Distance If we calculate slope from the formula:
![slope of a graph m generator slope of a graph m generator](https://d26tpo4cm8sb6k.cloudfront.net/img/slope.png)
To calculate the true run, we need to use the Pythagorean Theorem. The map distance is the true horizontal distance but the travel distance of 3.0009375 miles is the slope length or slope distance. However there is a small difference between the 3 mile distance measured on the map and the 3.0009375 miles (15,844.95 feet) we just traveled on the road. With an altimeter and an odometer, we travel the exact route we measured on the map and our altimeter indicates a change in altitude of 396 feet which, not surprisingly, is precisely what we had already measured on the map. Grade = (rise ÷ run) * 100 grade = (396 ÷ 15,840) * 100 = 2.5%Ĭalculating Grade By Measuring The Road Distance One way to calculate the grade of a hill is with a map that shows the altitudes of locations.įor example, you've measured out a distance of 3 miles (run) with a change in altitude of 396 feet (rise).įirst, the units must be made consistent, so we convert 3 miles to 15,840 feet. Stating this as an angle of 2.8624 degrees doesn't give you much of an idea how the rise compares to the run. Stating this as a percentage, whatever horizontal distance you travel, your altitude increases by 5% of that distance.
![slope of a graph m generator slope of a graph m generator](https://ncalculators.com/formula-images/geometry/slope-intercept-example.png)
Stating a ratio such as 1 in 20 tells you immediately that for every 20 horizontal units traveled, your altitude increases 1 unit. Of these 3 ways, slope is expressed as a ratio or a grade much more often than an actual angle and here's the reason why. Slope, tilt or inclination can be expressed in three ways:ġ) As a ratio of the rise to the run (for example 1 in 20)Ģ) As an angle (almost always in degrees)ģ) As a percentage called the " grade" which is the (rise ÷ run) * 100. Bicyclists, motorists, carpenters, roofers and others either need to calculate slope or at least must have some understanding of it.