Slope Calculator

About this calculator

The slope of a line through two points (x₁,y₁) and (x₂,y₂) measures how steeply it rises or falls: m = (y₂ − y₁) / (x₂ − x₁), often described as “rise over run.” A positive slope climbs left to right, a negative slope descends, a slope of 0 is perfectly horizontal, and an undefined slope (division by zero) marks a vertical line. The angle the line makes with the horizontal follows from it directly: θ = arctan(m).

Slope is one of the most widely applied ideas in coordinate geometry precisely because “rate of change” shows up everywhere: physicists read it as velocity on a position-time graph or acceleration on a velocity-time graph, economists read it as marginal cost or marginal rate on a supply/demand curve, and civil engineers use it directly to specify road grades and roof pitches. Accessibility standards like the ADA even define maximum allowable ramp slopes in exactly these rise-over-run terms.

Enter two points’ coordinates, and this calculator returns both the slope of the line through them and the angle it makes with the horizontal.