Slope Calculator
Find the slope, rise, run, angle and line equation through two coordinate points.
Result
Slope: 2
This coordinate slope is signed; a vertical line has an undefined slope.
- Rise (Y₂ − Y₁)
- 8
- Run (X₂ − X₁)
- 4
- Line angle
- 63.4349 °
- Line equation
- y = 2x + 0
https://calcgallery.com/everyday-math/slope-calculator/
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How to use the Slope Calculator
- Enter the x and y coordinates of two different points on a line.
- Read the slope as signed rise divided by signed run.
- Use the angle and line equation to describe the same line in other forms.
Slope from two coordinate points
The slope m of the line through (x₁, y₁) and (x₂, y₂) is:
m = (y₂ − y₁) / (x₂ − x₁)Once the slope is known, the calculator substitutes a point into y = mx + b
to find the y-intercept. A vertical line is the special case x₁ = x₂; its
slope is undefined and its equation is x = x₁.
The formulas follow OpenStax College Algebra 2e.
With your numbers
- Rise = 10 − 2 = 8.
- Run = 5 − 1 = 4; slope = rise ÷ run = 2.
Quick reference
This coordinate slope is signed; a vertical line has an undefined slope.
| Example | Slope |
|---|---|
| Slope of 2 | 2 |
| Horizontal line | 0 |
| Negative slope | -2 |
| Vertical line | Undefined (vertical line) |
| Fractional slope | 0.5 |
| Line through origin | 1 |
Common questions about the Slope Calculator
- What is the slope formula?
- Slope equals (Y₂ − Y₁) divided by (X₂ − X₁).
- What does a negative slope mean?
- The line falls as x increases from left to right.
- Why is a vertical slope undefined?
- Both points have the same x coordinate, so the run is zero and division by zero is undefined.
- Is this the same as construction grade?
- No. This page uses coordinate points. Use Slope and Grade Calculator for rise, run, percentage grade, and one-in-x ratios.