Enter two points on a line — X1, Y1 and X2, Y2 — and the Gradient Calculator computes the gradient (slope) of the line, along with the rise, run, and angle of inclination. Whether you're analyzing a ramp, a ski slope, or a graph, you get a complete picture of steepness in one step.
Gradient (Slope)
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Rise (ΔY)
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Run (ΔX)
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Angle of Inclination
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Percentage Grade
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Slope Direction
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The gradient (also called slope) measures how steep a line is between two points. It is defined as the ratio of the vertical change (rise) to the horizontal change (run). A steeper line has a larger gradient value.
The gradient formula is: gradient = rise / run = (Y2 − Y1) / (X2 − X1). Simply subtract the y-coordinates to get the rise and subtract the x-coordinates to get the run, then divide rise by run.
A 1/10 gradient means that for every 10 units of horizontal distance (run), the elevation changes by 1 unit (rise). This is equivalent to a 10% grade and an angle of approximately 5.71 degrees.
Using the formula rise = gradient × run, the rise equals 2 × 10 = 20. So if you travel 10 units horizontally along a line with gradient 2, you rise 20 units vertically.
A 20% gradient equals 0.2 as a decimal. Using run = rise / gradient, the run equals 2 / 0.2 = 10. So you travel 10 units horizontally for every 2 units of rise.
Yes. A negative gradient means the line slopes downward from left to right. For example, if Y decreases as X increases, the gradient will be negative. A gradient of zero means the line is perfectly horizontal.
The gradient is undefined when the run (ΔX) equals zero — that is, when X1 = X2. This represents a perfectly vertical line, which has no finite slope. The calculator will flag this condition to avoid division by zero.
The gradient is the ratio rise/run, while the angle of inclination is the arctangent of that ratio expressed in degrees. A gradient of 1 corresponds to a 45° angle. The angle gives a more intuitive sense of steepness for physical applications like ramps and roads.