Slope Calculator
Find the slope, distance, and midpoint between two points.
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About this calculator
How This Slope Calculator Works
Enter the coordinates of two points, and the calculator returns the slope of the line between them, along with the distance between the points and their midpoint.
Worked Example
For the points (1, 2) and (5, 10): the slope is 2 — for every 1 unit right, the line rises 2 units. The distance between the points is 8.94 units, and the midpoint is (3, 6).
The Formula
Slope (m) = (y₂ − y₁) ÷ (x₂ − x₁) — the change in y divided by the change in x, often described as "rise over run." Distance uses the Pythagorean theorem: d = √[(x₂ − x₁)² + (y₂ − y₁)²]. The midpoint is simply the average of the two x-coordinates and the average of the two y-coordinates.
Reading the Sign and Size of the Slope
- Positive slope — the line rises left to right
- Negative slope — the line falls left to right
- Slope of 0 — a horizontal line, no change in y
- Undefined slope — a vertical line, where x doesn't change and the rise-over-run formula divides by zero
Worked example
Between (1, 2) and (5, 10), the slope is 2 (a rise of 8 over a run of 4) — the line climbs 2 units for every 1 unit it moves right.
Frequently asked questions
What does a negative slope mean?
The line falls as it moves right — for every unit increase in x, y decreases. A positive slope rises left to right; a slope of 0 is a flat horizontal line.
Why is the slope "undefined" for a vertical line?
Slope is rise over run, and a vertical line has zero run (both points share the same x-coordinate) — dividing by zero is undefined, so vertical lines are simply described as having no slope rather than a slope of infinity.
What's the midpoint used for?
It's the point exactly halfway between the two coordinates — useful for finding the center of a line segment, such as the midpoint of a diameter when working with circles.