Online Tool Store
Slope Calculator
Enter two points to get the slope, y-intercept, line equation, angle, distance, and midpoint, with vertical lines handled properly. Runs in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Equation of the line
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Example shown — enter your own coordinates.
- Slope (m)
- Y-intercept (b)
- Angle from horizontal
- Distance between points
- Midpoint
- Rise / run
How it works
- Enter the coordinates of two points on the line.
- Everything updates as you type: slope, intercept, equation, angle, distance, and midpoint.
- Read the plain-English summary if you want a sanity check on direction and steepness.
- Copy the whole set of results in one go.
The formulas, worked through
Slope is the vertical change divided by the horizontal change, and everything else follows from it:
m = (y₂ − y₁) ÷ (x₂ − x₁) // rise over run
b = y₁ − m·x₁ // substitute a known point
θ = arctan(m) // angle from the horizontal
d = √((x₂ − x₁)² + (y₂ − y₁)²) // Pythagoras
Take the example on load, (1, 2) to (4, 8). The rise is 6 and the run is 3, so m = 2. Substituting gives b = 2 − 2×1 = 0, making the line y = 2x — it passes exactly through the origin. The angle is arctan(2) ≈ 63.43°, the distance is √45 ≈ 6.708, and the midpoint is (2.5, 5).
The distance formula is just Pythagoras with the two coordinate differences as the short sides, which is why a 3-across, 4-up step gives exactly 5.
The two cases most calculators get wrong
A horizontal line has a slope of exactly zero: the rise is nothing, so m = 0, and the equation is y = a constant. A vertical line is genuinely different — the run is zero, and dividing by it has no answer at all. The slope is undefined rather than infinite, there is normally no y-intercept, and the line has to be written as x = a constant because it cannot be expressed as y = mx + b at all.
A related edge case: if you enter the same point twice, there is no unique line through it — infinitely many pass through a single point — so the tool asks you to change a coordinate rather than returning a meaningless zero.
FAQ
What does the slope actually tell me?
How steep the line is, and which way it leans. A slope of 2 means the line climbs 2 units for every 1 unit across; −0.5 means it drops half a unit for every unit across. Zero is perfectly flat.
Why is a vertical line "undefined" rather than infinite?
Because working it out requires dividing by the horizontal change, and for a vertical line that change is exactly zero. Division by zero has no answer, so the slope does not exist — it is not a very large number. The tool says "undefined" and gives you the line as x = a constant instead.
Does the order of the two points matter?
No. Swapping them flips the sign of both the rise and the run, and those cancel out — so (1,2) to (4,8) and (4,8) to (1,2) both give a slope of 2. The distance and midpoint are unchanged too.
What is the y-intercept when my line is vertical?
There usually is not one. A vertical line only crosses the y-axis if it sits exactly on it, at x = 0 — in which case it overlaps the axis entirely. The tool reports "none" or "every value" accordingly rather than printing a misleading number.
How is the angle calculated?
It is the arctangent of the slope, measured from the horizontal. A slope of 1 is exactly 45°, a slope of 2 is about 63.43°, and a negative slope gives a negative angle meaning the line descends. Vertical lines are reported as 90°.
Why show rise over run as a fraction?
Because it is often more useful than a decimal — a 6/3 slope reduces to 2/1, and a gradient like 1/12 is exactly how ramps and roof pitches are specified. Whole-number coordinates get the reduced ratio automatically.
How we compare
| Feature | Online Tool Store | Ad-supported maths sites | Graphing calculator |
|---|---|---|---|
| Handles vertical lines correctly | ✓ | Many return Infinity or an error | ✓ |
| Angle, distance, and midpoint together | ✓ | Usually separate pages | ✓ |
| Reduced rise/run ratio | ✓ | ✗ | ✗ |
| No ads, nothing typed leaves the page | ✓ | ✗ | ✓ |
| Draws the line on a graph | ✗ | Some do | ✓ |
| Works with curves, not just straight lines | ✗ | ✗ | ✓ |
Handy for homework, for working out a ramp or roof gradient, and for any time you have two coordinates and need the line between them — with the vertical and identical-point cases answered honestly instead of returning a number that looks plausible. It does not plot anything; for that a graphing calculator is the right tool.