Slope Calculator

Calculate slope, angle, distance, midpoint, and line equation

Point 1 (x₁, y₁)

Point 2 (x₂, y₂)

Slope (m)

Angle of inclination

63.4349°

Distance

8.9443

Midpoint

(3, 6)

y-intercept (b)

Line equation

y = 2x + 0

How slope is calculated

The slope of a line through two points (x₁, y₁) and (x₂, y₂) is m = (y₂ − y₁) / (x₂ − x₁) — rise over run. This tool also computes the angle of inclination (arctan of the slope, in degrees), the Euclidean distance between the points (√((Δx)² + (Δy)²)), the midpoint, and the full slope-intercept equation y = mx + b where b = y₁ − mx₁. A vertical line has an undefined slope; a horizontal line has slope 0. All values round to 4 significant figures.

Built and maintained by Meet Shah · Last updated 19 July 2026

What this tool is used for

Finding the gradient between two coordinate points.
Getting the line equation from two points.
Working out an angle from a rise and a run.
Finding the midpoint and distance alongside the slope.
Checking a gradient against a plotted line to catch a sign error.

Frequently Asked Questions

What is the formula?: Rise over run: (y₂ − y₁) ÷ (x₂ − x₁). The order must match on top and bottom — subtracting the points in opposite orders flips the sign, which is the most common arithmetic slip and turns an uphill line into a downhill one.
Why is a vertical line undefined rather than infinite?: Because the run is zero and division by zero has no value. A vertical line genuinely has no slope in this sense; its equation is x = k, which cannot be written as y = mx + b at all.
How do slopes relate for parallel and perpendicular lines?: Parallel lines share a slope. Perpendicular ones have slopes whose product is −1, so the perpendicular to a line of slope 2 has slope −½ — the negative reciprocal. The vertical/horizontal pair is the exception, since one of them has no slope to reciprocate.
How does slope relate to a percentage grade?: A grade is the slope as a percentage: a slope of 0.08 is an 8% grade, which is a steep road. Roofers use a different convention again — "6 in 12" pitch means a rise of 6 per 12 of run, a slope of 0.5.
What does the intercept mean?: Where the line crosses the y-axis, the value of y when x is zero. In a real model that is the starting value before anything accumulates — and it is often meaningless in context, such as a fitted line predicting a weight at height zero.

Common errors and gotchas

Dividing rise by run in the wrong order, which inverts the gradient.
Reporting an undefined slope as zero for a vertical line, which are opposite cases.
Confusing the gradient with the angle, which needs an arctangent.
Mixing up the point order, which flips the sign of the difference but not of the slope.
Reading a percentage gradient as a ratio, which differ by a factor of a hundred.