Slope Calculator
Point 1
Point 2
Slope (gradient) measures the steepness of a line: rise over run = Δy/Δx = (y₂−y₁)/(x₂−x₁). Positive slope = rising left to right; negative = falling; zero = horizontal; undefined = vertical. Used in algebra, physics, road engineering, and data analysis.
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Tip: Road grade % = (rise/run) × 100. A 5% grade means 5 feet of elevation gain per 100 feet of horizontal distance. Most cars struggle above 20% grade.
- 1m = (y₂ − y₁) / (x₂ − x₁)
- 2Slope-intercept form: y = mx + b (m=slope, b=y-intercept)
- 3Parallel lines have equal slopes
- 4Perpendicular lines: slopes are negative reciprocals (m₁ × m₂ = −1)
Points (1, 2) and (4, 8)=Slope = (8−2)/(4−1) = 6/3 = 2For every 1 right, go 2 up
Slope of 1/4 in road engineering=25% grade1 ft rise per 4 ft run
| Application | Typical slope | Unit |
|---|---|---|
| ADA ramp (max) | 1:12 (8.33%) | Rise:run |
| Residential roof | 4:12 to 8:12 | Pitch |
| Highway grade (max) | 6–8% | % grade |
| Stair rise/run | 7:10 to 7:11 | Rise:run (inches) |
| Ski slope (beginner) | 5–25% | % grade |
| Ski slope (expert) | 40%+ | % grade |
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Fun Fact
The steepest street in the world is Baldwin Street in Dunedin, New Zealand at a 35% grade (19.3°). The steepest road legally driven by regular cars is Ffordd Pen Llech in Wales at 37.45%.
References
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