Slope Calculator
Enter the coordinates of two points and get the slope of the line through them, its angle of inclination, the y-intercept, the distance between the points, their midpoint and the line equation — all from the same four numbers.
The equation line rounds its coefficients to 4 decimal places; the numeric rows round to 2.
Formula and calculation
Worked example
For the points (2, 3) and (5, 9): the slope is 2, so the line rises 2 units for every 1 unit across, and it crosses the y-axis at -1. In slope-intercept form the line is y = 2x - 1, and its angle of inclination is 63.43°. The two points are 6.71 apart, and the midpoint between them is (3.5, 6).
Rise over run, grades and the angle of a slope
Slope is rise over run, and roads quote the same number as a percentage: a slope of 0.05 is a 5% grade, and the 1:12 ratio the ADA standards allow for a new wheelchair ramp is a slope of 0.0833, or 8.33%. The angle version of a slope is tan−1(m): 0.05 is about 2.9°, and a 45° line has a slope of exactly 1. One trap: on a falling line the angle of inclination is measured from the positive x-axis and lands between 90° and 180°, so a slope of −1 gives 135° — while the tan−1 button on a scientific calculator returns −45°. Both describe the same line; this page shows the inclination used in textbooks.
What the results mean
- Slope
- The slope of the line: how much y changes for every 1 unit that x increases. A slope of 2 means the line rises 2 units for every 1 across; a negative slope falls. A vertical line has no slope and shows undefined (vertical line).
- Y-intercept
- The y-intercept: the y-value where the line crosses the y-axis, at x = 0. It is undefined for a vertical line, which crosses the y-axis only when its equation is x = 0.
- Line equation
- The line in slope-intercept form, y = mx + b, with your numbers filled in — for example y = 2x - 1. Coefficients are rounded to 4 decimal places for display; a vertical line is written as x = c instead.
- Angle of inclination
- The angle of inclination: the angle between the line and the positive x-axis, measured counterclockwise from 0° up to just under 180°. Horizontal is 0°, a line rising at 45° is 45°, falling lines are past 90°, and a vertical line is 90°.
- Distance
- The straight-line distance between the two points, from the Pythagorean theorem: √((x₂ − x₁)² + (y₂ − y₁)²).
- Midpoint x
- The x-coordinate of the midpoint — the point exactly halfway between the two points: (x₁ + x₂) ÷ 2.
- Midpoint y
- The y-coordinate of the midpoint: (y₁ + y₂) ÷ 2. The midpoint sits on the line, which is a quick way to check that your coordinates are right.
Frequently asked questions
How do I find the slope of a line from two points?
Divide the vertical change by the horizontal change: m = (y₂ − y₁) ÷ (x₂ − x₁). For the points (2, 3) and (5, 9) that is (9 − 3) ÷ (5 − 2) = 6 ÷ 3 = 2, so the line rises 2 units for every 1 unit to the right.
What does an undefined slope mean?
It means the line is vertical: both points have the same x-value, so the run is zero and the rise-over-run fraction would divide by zero. The line still exists and is written x = c, but it has no slope, no y-intercept and no y = mx + b form — this page shows it as undefined (vertical line) instead of failing.
How do I convert a slope to degrees?
Take the arctangent of the slope: a slope of 1 is 45°, a slope of 2 is about 63.43°, and a slope of −1 is 135° as an angle of inclination. If you have a road grade instead, divide it by 100 first: an 8% grade is a slope of 0.08, about 4.57°.
How do I find the distance between two points?
Use the Pythagorean theorem on the horizontal and vertical gaps: distance = √((x₂ − x₁)² + (y₂ − y₁)²). From (2, 3) to (5, 9) the gaps are 3 and 6, so the distance is √(9 + 36) = √45, about 6.71.