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.

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Slope Visualization

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

Как использовать 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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