Slope Calculator

The slope, or gradient, of a line measures how steep it is: the change in y divided by the change in x, often called rise over run. This slope calculator finds the slope through two points as an exact fraction, then gives the line's equation, its angle with the x-axis and the perpendicular slope.

How to use the slope calculator

Enter the coordinates of the first point (x₁, y₁).
Enter the coordinates of the second point (x₂, y₂).
Press Calculate to see the slope and the equation of the line.

Formula

m = \frac{y_2 - y_1}{x_2 - x_1}

y = mx + c

Worked example: (1, 2) and (4, 8)

x₁: 1
y₁: 2
x₂: 4
y₂: 8

✓ Answer checked

m = 2

Equation of the line: $y = 2x$
Angle with the x-axis: $\approx 63.4349^\circ$
Perpendicular slope: $-\frac{1}{2}$

Slope = rise ÷ run = 6 ÷ 3 = 2.

Step-by-step working (4 steps)

Use the slope formula Slope formula
Slope is rise over run: the change in y divided by the change in x.
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute
Put the coordinates in.
$m = \frac{8 - 2}{4 - 1} = \frac{6}{3}$
Simplify
A positive slope means the line goes up from left to right.
$m = 2$
Find the y-intercept Slope-intercept form
Substitute one point into y = mx + c and solve for c.
$c = 2 - 2 \times 1 = 0$