Slope, Gradient & Angle Calculator
Find the slope between two points, convert between gradient formats, and get the line equation. Used in maths, construction, civil engineering, and navigation.
Slope and Gradient
Slope Formula
Slope (m) = Rise ÷ Run = (y₂−y₁) ÷ (x₂−x₁). Positive slope: line goes up left-to-right. Negative: goes down. Zero: horizontal. Undefined: vertical line (division by zero).
Gradient Formats
Slope as ratio: 1:20 means 1 unit up for every 20 across. As percentage: multiply ratio by 100 (5%). As angle: arctan(rise/run). A 5% road grade = 2.86° = 1:20 ratio. UK road signs use percentage grade.
Line Equation
y = mx + b. m is the slope. b (y-intercept) is found by substituting a known point: b = y₁ − m×x₁. Two points fully define a line — this calculator gives you the complete equation for both maths and graphing.
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