Slope Calculator (2026)

Calculate the slope (m), line equation, rise, run, angle of inclination in degrees, percentage grade, and Euclidean distance between any two coordinate points (x1, y1) and (x2, y2).

Quick Answer & Slope Formula

The slope of a line passing through coordinates (x₁, y₁) and (x₂, y₂) is defined as the vertical rise divided by the horizontal run:

m = (y₂ - y₁) / (x₂ - x₁) = Δy / Δx

If x₁ = x₂, the line is vertical and the slope is mathematically undefined. If y₁ = y₂, the line is horizontal and the slope is 0.

Derived Metrics

  • Angle of Inclination: θ = arctan(m) × (180 / π) in degrees.
  • Percentage Grade: Grade (%) = |m| × 100%.
  • Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).
  • Slope-Intercept Equation: y = mx + b, where b = y₁ - m(x₁).

Step-by-Step Example

Given Point 1 = (2, 3) and Point 2 = (6, 11):

  1. Calculate rise (Δy): 11 - 3 = 8
  2. Calculate run (Δx): 6 - 2 = 4
  3. Compute slope: m = 8 / 4 = 2.00
  4. Angle: θ = arctan(2.00) = 63.43°
  5. Distance: d = √(16 + 64) = √80 ≈ 8.944 units

Frequently Asked Questions

What is a negative slope?
A negative slope indicates that the line decreases from left to right: as x increases, y decreases.
How do I find slope on a construction roof?
Use our specialized Roof Pitch Calculator to convert pitch ratios (e.g. 4:12) to roof angles and rafter lengths.