Math Equations for Calculating the Grade Percent on a Vertical Rise

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There are various ways to express the steepness of an incline. One of these ways is the grade percent, which is equal to the slope of the incline multiplied by 100 percent. Grade percents are typically expressed as positive values regardless of whether the observer is looking up or down the incline.

Slope

  • Grade percent can be found by multiplying the slope of an incline by 100 percent. For example, if the slope of a hill is 1.5, the grade percent of the hill would be 1.5 x 100 percent = 150 percent.

Horizontal and Vertical Distances

  • The slope of a line is equal to the vertical distance divided by the horizontal distance. Since grade percent can be found by multiplying the slope by 100 percent, the grade percent of an incline is equal to 100 percent times the vertical distance divided by the horizontal distance. So, for example, if a ramp covers a vertical distance of 10 feet and a horizontal distance of 20 feet, the grade percent of the ramp would be 100 percent x 10/20 = 50 percent.

Ratio of Rise:Run

  • In certain situations, the information available will be given in the form of the ratio of rise:run. The rise is equal to the vertical distance covered by the incline, while the run is equal to the horizontal distance. So, for example, if a ramp covers a vertical distance of 10 feet and a horizontal distance of 20 feet, the rise:run ratio of the ramp would be 10/20 = 0.5. The rise:run ratio is equal to the slope, and so the grade percent is equal to rise/run x 100 percent.

Angle of Incline

  • The incline of a slope is often expressed as the angle that the incline makes with the ground. For example, a board lying flat on the ground makes an angle of 0 degrees, while a wall perpendicular to the ground makes an angle of 90 degrees. The grade percent can be calculated from the angle by using the equation grade percent = tan (angle) x 100 percent, where "tan" is the trigonometric tangent function.

References

  • Photo Credit Hemera Technologies/AbleStock.com/Getty Images
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