Slope Calculator
Calculate slope (gradient) between two points. Find slope, intercept, distance, and line equation for any two coordinate pairs.
1x² − 5x + 6 = 0
Discriminant = 1
two real roots
x = (−b ± √(b²−4ac)) / 2a
x₁ = 3
x₂ = 2
About the Slope Calculator
The slope of a line measures its steepness and direction — how much y changes for every unit change in x. Positive slope means the line rises left to right; negative slope means it falls. Slope appears in physics (velocity as slope of position-time graph), economics (marginal cost), engineering (grades of roads), and throughout coordinate geometry.
Formula
m = (y₂ − y₁) ÷ (x₂ − x₁) = rise ÷ run
How It Works
Slope m = (y₂ − y₁) / (x₂ − x₁) = rise / run. From slope and a point, the line equation is y − y₁ = m(x − x₁) (point-slope form), which converts to y = mx + b (slope-intercept form). Special cases: horizontal line has slope = 0; vertical line has undefined slope. Perpendicular lines have slopes that are negative reciprocals: m₁ × m₂ = −1.
Tips & Best Practices
- ✓Road grade (slope) of 6% means 6 feet of rise per 100 feet of horizontal run.
- ✓A slope of 1 (45°) means equal rise and run — a 1:1 pitch on a staircase.
- ✓Parallel lines have identical slopes; perpendicular lines have slopes that multiply to −1.
- ✓Average rate of change between two points equals the slope of the line through those points.
- ✓Calculus extends slope to curved functions — the derivative gives instantaneous slope at any point.
Who Uses This Calculator
Students completing coordinate geometry and algebra, civil engineers designing road grades and wheelchair ramps, architects determining roof pitches, data analysts fitting linear regression models, and physics students graphing motion all use slope calculations.
Optimised for: USA · Canada · UK · Australia · Calculations run in your browser · No data stored
Frequently Asked Questions
What is the slope formula?
Slope (m) = (y₂ - y₁) / (x₂ - x₁). For points (2,3) and (6,7): slope = (7-3)/(6-2) = 4/4 = 1.