How do I calculate the slope of a line?

Divide the change in y by the change in x. For the points 0,0 and 4,8 that is 8 minus 0 over 4 minus 0, which is 8 divided by 4, giving a slope of 2.

What is the formula for slope?

Slope equals (y2 minus y1) divided by (x2 minus x1). It is sometimes written as rise over run, where rise is the vertical change and run is the horizontal change.

How do I find the equation of a line from two points?

Find the slope first, then substitute one point into y equals slope times x plus b to get b. For 0,1 and 1,3 the slope is 2 and substituting gives b equals 1, so the line is y equals 2x plus 1.

What is the angle of inclination?

The angle the line makes with the positive x axis, measured anticlockwise. It is the arctangent of the slope, so a slope of 1 gives 45 degrees and a slope of 2 gives about 63.4 degrees.

What is the perpendicular slope?

The negative reciprocal of the slope, which is minus one divided by the slope. Two lines are perpendicular exactly when their slopes multiply to minus one, and this is why the perpendicular is a reciprocal rather than simply the opposite.

What happens with a vertical line?

The slope is undefined because a vertical line has no run, and dividing by zero is not defined. The line is instead written as x equals a constant, and its perpendicular is horizontal with a slope of zero.

How do I convert a road gradient percentage into a slope?

Divide by 100. A 6 percent gradient is a slope of 0.06, and its angle of inclination is the arctangent of 0.06, which is roughly 3.4 degrees.

What does a slope of 0.5 mean in practice?

The line rises 0.5 units vertically for every 1 unit horizontally. With metres on both axes that is a gradient of 0.5, or 50 percent, and an angle of inclination of about 26.6 degrees. In different axis units the same number means a different physical gradient.

Is a positive slope always an upward line?

No. A positive slope means y increases as x increases, which is a rise when read left to right on a conventional graph. If the axes are reversed, flipped in a screen design, or measured differently, the same positive slope can appear to fall.

Can two points give the same line regardless of order?

Yes. Swapping the two points changes the sign of both the rise and the run, and a fraction with both signs flipped has the same value. The line, slope, intercepts and angle are all unchanged.

How to Use the Slope Calculator

Enter any two points on a line and get the slope, the equation, the angle of inclination, both intercepts, the perpendicular slope and the midpoint in a single result.

Step-by-Step Instructions

1 Enter the x and y coordinates of your first point.
2 Enter the x and y coordinates of your second point. The order does not matter, since swapping the points gives the same slope.
3 Read the slope first, then the equation of the line and the angle of inclination.
4 Use the intercept tiles to find where the line crosses each axis, and the perpendicular tile for the normal to the line.
5 Use the How this is worked out panel to copy the rise over run calculation into your own working.

Understanding the Inputs

x1 and y1

The coordinates of the first point. Both values must be expressed in the same unit as the corresponding values of the second point.

How to find it: Two points read from a graph, a set of measurements, a map grid, or fitted data. Order between the two points does not affect any output.

Why it matters: Slope is rise over run, and both are differences. Using consistent units is what makes the ratio meaningful, and mixing them produces a number with no physical interpretation.

x2 and y2

The coordinates of the second point. If both points share the same x value the line is vertical and has no slope.

How to find it: Any second point lying on the same line. The further apart the points are, the more reliable the resulting slope as an estimate of the underlying trend.

Why it matters: The difference between the points is the entire calculation. Widely spaced points reduce the effect of measurement noise, which is why fitting a line uses the full spread of data rather than two adjacent points.

Tips & Best Practices

✓ Keep both axes in the same unit so the slope means something physical.
✓ Convert percentage grades to decimals by dividing by 100.
✓ Swap the points if it makes the subtractions easier to follow.
✓ Check perpendicular lines by confirming the two slopes multiply to minus 1.

Try the Slope Calculator

by CalculatorPro Tools · Updated 10-12-2026