Slope Calculator
Free slope calculator. Find the slope (m) between two points with rise-over-run formula, step-by-step solution, and line visualization. Browser-based privacy.
Slope Calculator
Free slope calculator. Find the slope (m) between two points with rise-over-run formula, step-by-step solution, and line visualization. Browser-based privacy.
1 Point 1
2 Point 2
Results
Slope (m)
Rise (Δy)
Run (Δx)
Line Equation
Angle (θ)
Chart
Step-by-Step Solution
Cómo usar esto Slope Calculator
Two-Point Input
Enter any two (x, y) coordinate pairs.
Instant Results
Get slope m, rise, run, angle, and line equation.
Step-by-Step
See the Δy, Δx, and full formula breakdown.
Vertical lines have undefined slope. Horizontal lines have slope = 0.
What Is Slope?
📐 Slope measures the steepness of a straight line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The formula is m = (y₂ − y₁) / (x₂ − x₁).
📊 Slope tells us the direction and rate of change:
- Positive slope — line goes up as you move right (increasing relationship)
- Negative slope — line goes down as you move right (decreasing relationship)
- Zero slope — horizontal line (no change in y)
- Undefined slope — vertical line (no change in x)
📐 Slope is the cornerstone of linear equations, regression analysis, physics (velocity), economics (marginal cost), and engineering (gradients).
How to Calculate Slope
- 1 Identify two points: Label your coordinates P₁ = (x₁, y₁) and P₂ = (x₂, y₂).
- 2 Calculate Rise (Δy): Subtract the y-coordinates: Δy = y₂ − y₁. This is the vertical distance between the two points.
- 3 Calculate Run (Δx): Subtract the x-coordinates: Δx = x₂ − x₁. This is the horizontal distance between the two points.
- 4 Divide Rise by Run: The slope m = Δy / Δx. If Δx = 0, the slope is undefined (vertical line).
- 5 Find the line equation: Using point-slope form y − y₁ = m(x − x₁), rearrange to y = mx + b where b = y₁ − m·x₁.
When to Use Slope
- You need the rate of change between two known data points
- You want to find the steepness of a line in geometry or physics
- You need the angle of inclination: θ = arctan(m)
- You want to write the equation of a line through two points
When Slope Is Undefined
- When x₁ = x₂ — the line is vertical and slope is undefined
- When dealing with curved (nonlinear) relationships — use regression instead
- When you have more than two points — use linear regression for a best-fit line
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