Slope Calculator
Slope, line equation, distance, midpoint, and angle from two points
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
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Quick summary
Enter two points (x₁, y₁) and (x₂, y₂) to find the slope — rise over run, (y₂−y₁)/(x₂−x₁) — plus the line's equation in y = mx + b form, the distance between the points, their midpoint, and the line's angle. For (1, 2) and (3, 6) the slope is 2, the equation is y = 2x, the distance is 4.47, and the midpoint is (2, 4). A vertical line (x₁ = x₂) has an undefined slope.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Frequently asked questions
How do I find the slope between two points?
Divide the change in y by the change in x: slope = (y₂ − y₁) / (x₂ − x₁), often called 'rise over run.' For (1, 2) and (3, 6): (6−2)/(3−1) = 4/2 = 2. This calculator also gives the full line equation, distance, and midpoint.
What is the equation of a line through two points?
Find the slope m, then the y-intercept b using b = y − mx with either point. The line is y = mx + b. For slope 2 through (1, 2), b = 2 − 2(1) = 0, so y = 2x. The tool builds this equation for you.
Why is a vertical line's slope undefined?
A vertical line has the same x for both points, so the run (x₂ − x₁) is zero, and dividing by zero is undefined. Such a line is written x = k rather than y = mx + b. The calculator flags this case.
How do I find the midpoint and distance?
The midpoint is the average of the coordinates: ((x₁+x₂)/2, (y₁+y₂)/2). The distance uses the Pythagorean theorem: √((x₂−x₁)² + (y₂−y₁)²). This calculator returns both alongside the slope.
Key terms
- Slope
- Rise over run — (y₂−y₁)/(x₂−x₁); the steepness of a line.
- Y-Intercept
- Where the line crosses the y-axis (the b in y = mx + b).
- Midpoint
- The point halfway between two points.
- Distance Formula
- √((x₂−x₁)² + (y₂−y₁)²) — the straight-line distance.
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.