Slope Calculator – Gradient from Two Points

Slope is rise over run — how fast y climbs per unit of x. Through (2,3) and (6,11), the rise is 11−3 = 8 and the run is 6−2 = 4, so m = 8/4 = 2: the line rises 2 units for each step right. The inclination angle follows from arctan(2) ≈ 63.43°, which roofers and ramp designers use directly. The calculator classifies the result — positive like +2 (rising), negative (falling), zero (horizontal), or undefined (vertical, when x₂−x₁ = 0). It also computes the perpendicular slope −1/m = −0.5, the number a normal line must carry, and the y-intercept b = y₁ − m·x₁ = 3 − 2×2 = −1, completing the equation y = 2x − 1.

1. 1

   Enter two points

   Provide (x₁,y₁) and (x₂,y₂) on the line

2. 2

   Compute rise and run

   Rise = y₂−y₁, run = x₂−x₁, both displayed

3. 3

   Divide for slope

   m = rise/run, classified as rising, falling, flat or vertical

4. 4

   Derive angle & intercept

   θ = arctan(m) and b = y₁ − m·x₁ complete the line equation

• 1

  m = 0 is horizontal; undefined slope (run 0) is vertical

• 2

  Parallel lines share m; perpendicular lines satisfy m₁ × m₂ = −1

• 3

  The angle in degrees is arctan(m), not m itself

• Flipping the formula to (x₂−x₁)/(y₂−y₁), which inverts the slope

• Subtracting inconsistently: (y₂−y₁) must pair with (x₂−x₁)

• Treating a vertical line as slope 0 — it has no slope (undefined)

• Forgetting the sign flip for perpendicular slopes, −1/m not 1/m