Slope Calculator
Find the slope, y-intercept, line equation, distance, and angle between two points.
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
About Slope Calculations
The slope of a line measures its steepness and direction. Mathematically, slope m = (y₂−y₁)/(x₂−x₁), often described as "rise over run." A positive slope means the line goes up from left to right; negative means it goes down. A slope of zero is horizontal, and an undefined slope (vertical line) occurs when x₁ = x₂.
The slope-intercept form of a line, y = mx + b, uses the slope m and the y-intercept b (where the line crosses the y-axis). Given two points, you can calculate b using b = y₁ − m×x₁ after finding the slope. This equation completely describes the line and allows you to find any y-value for a given x-value, or vice versa.
The angle of inclination θ = arctan(m) converts the slope into an angle measured from the positive x-axis. This is useful in engineering and physics where directions are often expressed as angles. Slopes appear in calculus as derivatives, in economics as marginal rates, in physics as velocity on position-time graphs, and in everyday contexts like road grades and roof pitches.
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For a related calculation, use Ratio Calculator to simplify ratios, solve for missing values in proportions, or scale a ratio by a factor. Alternatively, use Distance Calculator to calculate the distance between two points in 2D or 3D space, plus midpoint and slope.