Rise Over Run Calculator

Rise over run is a way to express the slope of a line or incline. The 'rise' refers to the vertical change (Δy) between two points, and the 'run' refers to the horizontal change (Δx). Dividing rise by run gives you the slope, which describes how steep a line is.

The formula is: slope = rise / run = Δy / Δx. When using two coordinate points, slope = (y2 − y1) / (x2 − x1). A positive slope means the line goes up from left to right, while a negative slope means it goes down.

Pick any two points on the line. The rise is the vertical distance between them — count the units up or down. The run is the horizontal distance — count the units left or right. Dividing rise by run gives the slope at any point along a straight line.

Use the inverse tangent (arctan) function: angle = arctan(rise / run). This gives you the angle of inclination in degrees from the horizontal. For example, a slope of 0.75 corresponds to an angle of about 36.87°.

Rise over run is used in construction, road design, roofing, and landscaping to measure steepness. Roofers use it to calculate roof pitch, civil engineers use it to design road grades, and architects use it for ramp accessibility compliance.

Slope as a decimal is the raw ratio of rise to run (e.g. 0.25). Slope as a percentage multiplies that ratio by 100 (e.g. 25%). Percentage grade is commonly used in road and trail design to indicate steepness.

A slope of 0 means the line is perfectly horizontal — there is no rise, only run. A vertical line, on the other hand, has an undefined slope because the run equals zero and division by zero is not possible.

Yes. A negative slope means the line descends from left to right. This happens when the rise is negative (y decreases as x increases) or the run is negative (moving in the opposite horizontal direction). The calculator handles negative values correctly.