Slope Calculator

Calculate Slope Between Two Points

Understanding Slope

Slope measures the steepness and direction of a line. It tells you how much y changes for every unit change in x — often described as "rise over run".

Types of Slope

Slope-Intercept Form

This is the most common way to write a linear equation. m is the slope and b is the y-intercept (where the line crosses the y-axis at x=0).

Related Formulas

• Angle: θ = arctan(m) — the angle the line makes with the x-axis
• Distance: d = √[(x₂-x₁)² + (y₂-y₁)²] — Pythagorean theorem
• Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2) — point halfway between

Real-World Slope Examples

• Road grades: A 6% grade means 6 feet of rise per 100 feet of run (slope = 0.06)
• Wheelchair ramps: ADA requires max 1:12 ratio (slope ≈ 0.083)
• Roof pitch: A 4/12 roof rises 4 inches per 12 inches horizontal (slope = 0.33)
• Stairs: Typical stairs have slope between 0.58 and 0.70

Frequently Asked Questions

What does a slope of 2 mean?

A slope of 2 means for every 1 unit you move right (run), the line goes up 2 units (rise). It's a fairly steep uphill line.

Can slope be a fraction or decimal?

Yes! Slope can be any real number. A slope of 0.5 means the line rises 1 unit for every 2 units of horizontal movement.

What's the slope of parallel lines?

Parallel lines have the same slope. If one line has m=3, all lines parallel to it also have m=3.

What's the slope of perpendicular lines?

Perpendicular lines have slopes that are negative reciprocals. If one line has m=2, a perpendicular line has m=-1/2 (their product equals -1).

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Slope Calculator FAQ