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How to use
The slope calculator turns two coordinate points into the main properties of their straight line: rise, run, slope, inclination angle, percent grade, line equation, y-intercept, midpoint and point-to-point distance.
- Enter the two coordinate pairs without mixing x and y between points.
- The calculator finds Δy and Δx.
- When Δx is non-zero it computes slope and the y=mx+b equation.
- For a vertical line it labels slope undefined and reports x = constant instead of dividing by zero.
How it is calculated
Example
For points (1, 2) and (5, 10), Δy = 8 and Δx = 4, so m = 2. The intercept is 0, the line is y = 2x, and the point-to-point distance is √80 ≈ 8.9443.
Important notes
Zero slope is horizontal; a vertical line has undefined slope, not zero slope. Percent grade here is the direct mathematical m×100. Road, roof or accessibility standards can add direction and domain-specific conventions, so the number alone should not be treated as a compliance result.
Worked examples and interpreting results
The line through (1,2) and (3,6) rises four units over a horizontal run of two, giving slope 2 and equation y=2x. Slope is vertical change divided by horizontal change.
| Case | Calculation | Result |
|---|---|---|
| Slope | (6 − 2) ÷ (3 − 1) | 2 |
| Y-intercept | 2 − 2 × 1 | 0 |
How to check the result
Equal x coordinates give a vertical line with undefined slope, not zero slope. Zero slope describes a horizontal line. Reverse the point order in both numerator and denominator to preserve the result.
Frequently asked questions
Does a vertical line have slope zero?
No. Its run is zero, so slope is undefined. A horizontal line has slope zero.
Does swapping the two points change slope?
No. Both rise and run change sign, leaving their ratio unchanged.
What is the inclination angle?
For a non-vertical line it is arctan(m), the angle associated with the line’s slope relative to the horizontal axis.