Calculate average slope between two points, or find grade percentage, angle, and a second point from rise, run, distance, and slope.
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Average Slope Formula
The following formula is used to calculate the Average Slope (average rate of change) between two points.
AS = (y_2 - y_1) / (x_2 - x_1)
- Where AS is the average slope (Δy/Δx, i.e., rise/run)
- (x₁, y₁) is the first point
- (x₂, y₂) is the second point
To calculate an average slope between two points, compute the rise (y₂ − y₁) and the run (x₂ − x₁), then divide rise by run. If you are averaging slopes across multiple segments with different run lengths, the correct “overall” average slope is total rise divided by total run (a run-weighted average), not a simple arithmetic mean of slope values.
How to Calculate Average Slope?
The following example problems outline how to calculate Average Slope.
Example Problem #1:
- First, determine the first point (x₁, y₁).
- The first point is given as: (2, 3).
- Next, determine the second point (x₂, y₂).
- The second point is provided as: (8, 15).
- Finally, calculate the Average Slope using the equation above:
AS = (y₂ − y₁) / (x₂ − x₁)
The values given above are inserted into the equation below and the solution is calculated:
AS = (15 − 3) / (8 − 2) = 12 / 6 = 2 (units of y per unit x)
Example Problem #2:
For this problem, the variables needed are provided below:
rise = 6
run = 8
This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer.
AS = rise / run = ?
