Slope Calculator
Calculate the slope, distance, and midpoint between two points on a coordinate plane.
What slope tells you
Slope measures steepness — how much y changes for every unit change in x. A positive slope rises left to right, a negative slope falls left to right, a slope of zero is a perfectly horizontal line, and an undefined slope (when x doesn't change at all) represents a vertical line.
Slope is calculated as 'rise over run' — the change in y divided by the change in x between two points, which is exactly what this calculator computes from your coordinates.
Distance and midpoint formulas
The distance between two points uses the Pythagorean theorem — treating the horizontal and vertical differences as the two legs of a right triangle, with the direct distance as the hypotenuse. This is why the distance formula looks like the Pythagorean theorem rearranged.
Midpoint is simply the average of the two x-coordinates and the average of the two y-coordinates — the point exactly halfway between the two given points. For more worked examples, see our slope calculator guide.
Frequently asked questions
What does an undefined slope mean?
It means the line is perfectly vertical — since slope requires dividing by the change in x, and a vertical line has no change in x, the division is undefined.
How is the distance formula related to the Pythagorean theorem?
The distance formula is essentially the Pythagorean theorem applied to coordinate geometry — the horizontal and vertical differences between two points form the legs of a right triangle, and the direct distance is the hypotenuse.
How do you calculate slope between two points?
Slope (m) = (y₂ - y₁) / (x₂ - x₁). This is called 'rise over run' — the vertical change divided by the horizontal change. For points (2, 3) and (6, 11): slope = (11-3) / (6-2) = 8/4 = 2.
What does slope tell you?
Slope tells you how steep a line is and which direction it goes. A positive slope means the line rises left to right. A negative slope means it falls. A slope of 0 is horizontal. An undefined slope is vertical. The steeper the line, the larger the absolute value of the slope.
What does slope calculation mean?
Slope calculation finds the steepness and direction of a line. Slope (m) = rise / run = (y₂-y₁) / (x₂-x₁). A positive slope rises from left to right. A negative slope falls. Zero slope is horizontal. Undefined slope is vertical.
How do you calculate slope with a formula?
The slope formula between two points (x₁,y₁) and (x₂,y₂) is: m = (y₂-y₁)/(x₂-x₁). Example: points (2,3) and (6,11) give slope = (11-3)/(6-2) = 8/4 = 2. A slope of 2 means the line rises 2 units for every 1 unit it moves right.