Slope Formula Calculator: Rise Over Run Between Two Points
Slope between two points
m = (y₂ − y₁) ÷ (x₂ − x₁)
First point x₁ · First point y₁ · Second point x₂ · Second point y₂
Read the two labelled points without changing their coordinates.
m = (y₂ − y₁) ÷ (x₂ − x₁)
The points are translated and scaled together to fit the drawing; the labels retain your actual coordinates.
Worked example you can change
Slope = (y₂ − y₁) ÷ (x₂ − x₁)
- Slope = (8 − (2)) ÷ (4 − (1))
- Slope ≈ 2
Calculator
Enter complete decimal numbers; separate list values with commas or spaces. Decimal answers are shown to 15 significant digits; exact integer results retain all digits.
- Rise
- 6
- Run
- 3
- Slope
- 2
Formula variants
| Shape or method | Formula | Meaning |
|---|---|---|
| Two points | m = (y₂ − y₁)/(x₂ − x₁) | Subtract in the same point order in numerator and denominator. |
| Horizontal line | rise = 0, run ≠ 0 ⇒ m = 0 | A horizontal line has no vertical change. |
| Vertical line | run = 0, rise ≠ 0 ⇒ undefined | Division by zero does not produce a finite slope. |
| Coincident points | rise = run = 0 ⇒ indeterminate | One point alone does not determine a unique line. |
Questions
What is the slope formula?
Slope is the difference in y divided by the difference in x: (y₂ − y₁)/(x₂ − x₁). Use the same point order in both differences.
Why is a vertical line’s slope undefined?
Its horizontal run is zero, so rise divided by run would require division by zero.
What if the points are the same?
Both rise and run are zero. Infinitely many lines pass through the same single point, so the slope is indeterminate.
Where can I find distance and midpoint?
Use the distance and midpoint calculator linked from the Math hub; it uses the same two-point coordinate convention.
Sources and method
Find slope from two points using signed rise over signed run. Vertical and coincident points have explicit explanations instead of a misleading number.
We calculate with 40 significant digits and round only the displayed result. Diagrams are labelled explanations and are not measurement drawings.
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