Slope Calculator
Compute the slope of the line through two points, plus its angle with the x-axis, with a worked example and special cases for vertical and horizontal lines.
Results
Slope m
- Angle with +x axis
- 63.4349°
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Educational estimates · not financial advice · free, no signup
Formula / how it works
Slope m = (y₂ − y₁) ÷ (x₂ − x₁) = rise ÷ run. Angle with the x-axis θ = arctan(m). A vertical line (x₁ = x₂) has undefined slope.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Slope describes how steep a line is: how many units it rises (or falls) vertically for each unit it runs horizontally. A slope of 2 means that for every 1 unit you move right, you go up 2. Positive slopes rise to the right, negative slopes fall, and zero slope is a horizontal line. This calculator takes two points and returns the slope and the angle the line makes with the positive x-axis. It is used in algebra, in graphing, in road and roof grades, and in analysing trends. A vertical line has no defined slope because the run is zero.
When to use / who it helps
- You need the steepness of a line through two points.
- You are finding the equation of a line.
- You are checking if two lines are parallel or perpendicular.
- You are converting a grade or pitch into an angle.
- You are analysing the trend between two data points.
How to use
Steps
- Enter x₁ and y₁ for the first point.
- Enter x₂ and y₂ for the second point.
- Read the slope m.
- Read the angle in degrees.
- Use y − y₁ = m(x − x₁) to write the line equation.
- Check that x₁ and x₂ are not equal.
How to interpret results
- Positive slope: the line goes up to the right; negative: down to the right.
- Zero slope is horizontal.
- Parallel lines share the same slope; perpendicular lines have slopes whose product is −1.
- The angle is measured from the positive x-axis.
- The scale of the axes affects how steep a graph looks, not the slope value.
Common mistakes & gotchas
- Subtracting in a different order for x and y.
- Dividing run by rise.
- Using a vertical line and expecting a number.
- Mixing units on the two axes.
- Confusing slope with percentage grade.
Worked example
Worked example — points (1, 2) and (4, 8)
- Rise: 8 − 2 = 6.
- Run: 4 − 1 = 3.
- Slope: 6 ÷ 3 = 2.
- Angle: arctan(2) ≈ 63.43°. A perpendicular line would have slope −1/2.
Result: The slope is 2, and the line makes an angle of about 63.43° with the x-axis.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Slope m = (y₂ − y₁) ÷ (x₂ − x₁) = rise ÷ run. Angle with the x-axis θ = arctan(m). A vertical line (x₁ = x₂) has undefined slope.
Frequently asked questions
What is the slope formula?
m = (y₂ − y₁) ÷ (x₂ − x₁).
What is the slope of a vertical line?
Undefined, because the run is zero.
How do I find the angle from the slope?
Take the inverse tangent of the slope.
How do I find a perpendicular slope?
Take the negative reciprocal: −1 ÷ m.
How is slope related to percent grade?
Percent grade is slope times 100, so a slope of 0.05 is a 5% grade.
Does the order of the points matter?
Not if you subtract in the same order for both coordinates.