What is slope?
Slope, written as m, measures how steep a line is. It is defined as the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on a line. A larger slope means a steeper line; a slope of zero is perfectly flat, while a negative slope falls from left to right.
How to use this calculator
Read the rise and run straight off your graph. The rise is how far the line moves up (positive) or down (negative) between two points; the run is how far it moves horizontally to the right. Enter both numbers and the calculator returns the slope, the equivalent percent grade, and the angle of incline in degrees.
The formula explained
The core equation is $$m = \frac{\text{Rise}}{\text{Run}}$$ Because dividing by zero is undefined, a run of 0 represents a vertical line whose slope is undefined (this tool reports 0 in that case). To express the same steepness as a percentage, multiply the slope by 100 to get the percent grade: $$\text{Percent} = \frac{\text{Rise}}{\text{Run}} \times 100\%$$ To get the incline angle, take the arctangent: $$\theta = \tan^{-1}\!\left(\frac{\text{Rise}}{\text{Run}}\right) \times \frac{180}{\pi}$$
Worked example
Suppose a line rises 4 units while running 2 units to the right. Then $$m = \frac{4}{2} = 2$$ As a percent grade that is \(2 \times 100 = 200\%\), and the angle of incline is \(\tan^{-1}(2) \approx 63.43^\circ\).
FAQ
What does a negative slope mean? The line goes downhill from left to right — the rise is negative.
What if the run is zero? The line is vertical and its slope is undefined, since you cannot divide by zero.
How do I find rise and run from a graph? Pick two clear points on the line, count the vertical distance between them for the rise and the horizontal distance for the run.
