What Is Percent Grade?
Percent grade (also called the slope percentage) describes how steep a line, road, ramp, or roof is. It is the vertical change (rise) divided by the horizontal change (run), multiplied by 100. A 10% grade means the surface climbs 10 vertical units for every 100 horizontal units. This calculator works with any pair of (X, Y) coordinates and is unit-agnostic — meters, feet, or any consistent unit.
How to Use It
Enter the X and Y coordinates of two points. Point 1 is the start and Point 2 is the end. The tool computes the rise (\(\Delta y = y_2 - y_1\)), the run (\(\Delta x = x_2 - x_1\)), the slope ratio, the percent grade, and the angle of incline in degrees.
The Formula Explained
Slope is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Multiply by 100 to convert to percent grade:
$$\text{Grade \%} = \frac{Y_2 - Y_1}{X_2 - X_1} \times 100\%$$The angle is found with arctangent of the slope. Note that grade and angle are not the same: a 100% grade equals a 45° angle, not 90°.
Worked Example
For Point 1 = (0, 0) and Point 2 = (200, 30): rise = 30, run = 200, slope =
$$\frac{30}{200} = 0.15$$grade = 15%, and the angle is \(\arctan(0.15) \approx 8.53°\).
FAQ
Is percent grade the same as the angle? No. Grade is rise/run as a percent; angle is the arctangent of that ratio. They only line up for small slopes.
What if the run is zero? A vertical line has an undefined slope; this tool reports a 90° angle for that case.
Can grade exceed 100%? Yes. When the rise is greater than the run, the grade is above 100% and the angle exceeds 45°.
