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Coordinate geometry line solver

Slope Calculator with Line Equation and Angle

Find slope from two points, from a standard-form equation, or from rise and run. The result includes reduced rise/run, slope-intercept and point-slope forms, inclination angle, midpoint, point distance and intercepts, with correct handling of vertical and horizontal lines.

Define the line

Slope and line results

Slope, equation and line geometry guide

This slope calculator provides a dedicated calculation workflow rather than a generic converter. Slope describes the change in y for each unit change in x. A complete line description also needs a point or an intercept, so the calculator reports several equivalent equation forms.

Slope from two points

Subtract y-coordinates in the same order as x-coordinates. Reversing both subtraction orders gives the same slope, but mixing the orders changes the sign incorrectly.

Vertical and horizontal lines

A horizontal line has zero rise and slope 0. A vertical line has zero run, so division by zero makes its slope undefined; its equation is x = constant rather than y = mx + b.

Standard form conversion

For Ax + By = C with B not zero, slope is −A/B and y-intercept is C/B. If B is zero, the equation represents a vertical line.

Angle, distance and midpoint

The inclination angle is arctangent of slope, adjusted to the 0°–180° line direction. Distance uses the Pythagorean formula, and midpoint averages the coordinates.

Reduced rise over run

When input differences are integers, the calculator divides rise and run by their greatest common divisor and normalizes the sign, producing the smallest integer direction vector.

What is the slope of a vertical line?

It is undefined because the run is zero and division by zero is not defined.

Can two different equations describe the same line?

Yes. Slope-intercept, point-slope and standard forms can represent the same geometric line.

Why can the angle be negative in some calculators?

Arctangent may return a signed direction; this tool normalizes line inclination to the conventional 0° through 180° range.