Algebra and Number

Slope Calculator

Measure the steepness and direction of the line joining two coordinate points, with angle and distance alongside slope.

Slope—
Inclination angle—
Point-to-point distance—

How to find slope from two points

  1. Enter the x and y coordinates of the first and second points.
  2. Read rise (change in y), run (change in x), and their ratio m = rise/run.
  3. Use the inclination angle and straight-line distance for geometric context. A zero run gives a vertical line with undefined slope.

Slope formula, angle, distance, and examples

Slope m = (y₂ - y₁)/(x₂ - x₁) is rise divided by run. A positive slope rises from left to right; a negative slope falls from left to right. For (0, 0) and (3, 4), rise is 4 and run is 3, so m = 4/3, about 1.33333.

The inclination angle is measured counterclockwise from the positive x-axis to the line, expressed from 0° up to but not including 180°. For the 3-4 example it is arctan(4/3), approximately 53.1301°. Reversing the two endpoints represents the same line and therefore keeps the displayed inclination.

Point-to-point distance is √[(x₂ - x₁)² + (y₂ - y₁)²]. A 3-unit run and 4-unit rise make a 5-unit distance. Distance uses the same coordinate unit as the inputs; slope is unitless only when both axes share the same unit.

When run is zero and rise is nonzero, the line is vertical: its slope is undefined, its inclination is 90°, and its distance is the absolute rise. When both run and rise are zero, the inputs describe one point, so no unique line or inclination exists. For an equation in point-slope form, use the related equation-focused tool.

Inputs and results

ItemMeaningCheck
Point 1First coordinate pair (x₁, y₁).Any finite real coordinates are allowed.
Point 2Second coordinate pair (x₂, y₂).Must differ from Point 1.
SlopeRise divided by run.Undefined when run is zero.
Angle and distanceLine inclination and endpoint separation.Angle is 0° to less than 180°; distance uses coordinate units.

Practical uses and limitations

Graph interpretation

Quantify the rise per unit of horizontal movement between two plotted points.

Road or ramp sketches

Compare an idealized grade after ensuring horizontal and vertical dimensions share a unit.

Coordinate checks

Use the angle and distance to inspect whether a plotted segment matches a geometric expectation.

Limits

Slope is an exact property of two ideal points, not a regression estimate for noisy data. Latitude and longitude require geodesic treatment for physical distance.

Frequently asked questions

What is an undefined slope?

It occurs when x₁ = x₂ and y₁ differs from y₂. Division by zero prevents a finite rise/run ratio.

Is zero slope the same as undefined slope?

No. Zero slope is a horizontal line with zero rise and nonzero run; undefined slope is vertical with zero run.

Why is angle shown separately?

Slope is a ratio; the angle is the geometric inclination of the line relative to the positive x-axis.

Does swapping the points change slope?

No. Both rise and run change sign, leaving their ratio and the unoriented line angle unchanged.

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Last reviewed: October 26, 2026. Calculations run in your browser. Check rounding and assumptions before using a result in consequential work.

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