Rise (Δy)6
Run (Δx)3
Slope2
y-intercept0
Angle63.43°

The formula

m=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}
m — slope (rise over run)
(x₁, y₁) — the first point
(x₂, y₂) — the second point
b — y-intercept, where the line crosses the y-axis

How it works

The slope of a line measures how steep it is — the change in y for each step in x. Enter two points and the calculator finds the slope, the angle of the line, and the equation that passes through both.

FAQ

What does a negative slope mean?

A negative slope means the line goes downhill from left to right: as x increases, y decreases. A slope of zero is a flat, horizontal line.

Why can the slope be undefined?

If both points share the same x value the line is vertical, and the run is zero. Dividing by zero is undefined, so a vertical line has no finite slope.

What does a slope of 1 mean?

A slope of 1 means the line rises exactly as much as it runs — for every step right, it moves up the same amount, giving a 45° angle. Slopes greater than 1 are steeper than that, and slopes between 0 and 1 are shallower.

Does the order of the two points matter?

No — swapping which point you call (x₁, y₁) and which you call (x₂, y₂) flips the sign of both the rise and the run, so the slope comes out the same either way.

How do I convert slope to a percentage grade?

Multiply the slope by 100 to get a percentage grade, so a slope of 0.05 is a 5% grade. This is the convention used for road and ramp inclines rather than the angle in degrees.

What is the difference between slope and the y-intercept?

Slope describes how steep a line is, while the y-intercept, b, is simply the point where the line crosses the y-axis. Together they define the line completely through the equation y = mx + b.

How does slope relate to parallel and perpendicular lines?

Parallel lines always share the same slope. Perpendicular lines have slopes that are negative reciprocals of each other, so a line with slope 2 meets one with slope −0.5 at a right angle.

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About the slope calculator

This calculator finds the slope of a straight line from two points, along with the line’s angle and its equation. Slope is one of the core ideas in algebra and geometry: it captures how quickly a line rises or falls. Whether you are plotting a graph, reading a chart or measuring a physical incline, the slope is the single number that tells you how steep the line is and in which direction it tilts.

How to use it

Enter the coordinates of two points on the line, each as an x and a y value. The calculator returns the slope, written as rise over run, plus the angle the line makes with the horizontal and the full equation y=mx+by = mx + b. For example, the points (1, 2) and (4, 8) give a slope of 2, because y rises 6 while x runs 3. A larger slope means a steeper line; a negative one means it heads downward.

The formula

Slope is the change in y divided by the change in x between the two points: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, often remembered as “rise over run”. The y-intercept then comes from b=y1−mx1b = y_1 - m x_1, giving the line’s equation y=mx+by = mx + b. The angle of the line is θ=arctan⁡(m)\theta = \arctan(m). If x2=x1x_2 = x_1 the denominator is zero and the slope is undefined, which corresponds to a vertical line.

Where it is used

Slope shows up far beyond the maths classroom. Builders and civil engineers use it for the gradient of roads, ramps and drainage, where it is often written as a percentage or a ratio. In science, the slope of a graph is a rate — speed on a distance-time plot, or the reaction rate in chemistry. Economists read slopes as marginal change, and anyone reading a chart uses slope instinctively to judge whether a trend is rising or falling and how fast.