Gradient Calculator
Calculate the gradient between two points on a line. This tool gives you the slope, rise, run, angle of inclination, and percentage gradient all at once.
The gradient (or slope) measures how steep a line is. It is the ratio of the vertical change to the horizontal change between two points.
The Formula:
Gradient = Rise / Run = (y2 - y1) / (x2 - x1)
Example:
For points (2, 3) and (8, 15):
- Rise = 15 - 3 = 12
- Run = 8 - 2 = 6
- Gradient = 12 / 6 = 2
This means the line goes up 2 units for every 1 unit it moves to the right.
Percentage Gradient:
Multiply the gradient by 100 to get a percentage. A gradient of 0.12 means a 12% grade. This format is commonly used for road signs, railway grades, and accessibility ramps.
Interpreting the Gradient:
- Positive gradient: The line rises from left to right (uphill)
- Negative gradient: The line falls from left to right (downhill)
- Zero gradient: The line is horizontal (flat)
- Undefined gradient: The line is vertical (run = 0)
Angle of Inclination:
The angle the line makes with the positive x-axis is found using arctan(gradient). A gradient of 1 corresponds to a 45° angle. In construction and civil engineering, this angle determines structural feasibility.