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Rise Over Run Slope Calculator — result sheet
Calculate rise, run, slope, direction angle, and y-intercept from two Cartesian points, while identifying a vertical line safely.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Rise= y₂−y₁; run=x₂−x₁; slope=m=rise/run when run is nonzero; y-intercept=b=y₁−mx₁.
Slope is a directed change in vertical position divided by directed change in horizontal position. The calculator keeps rise and run visible, reports the line's direction angle, and does not invent a finite slope for a vertical line.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Point 1 x — minimum -1000000000; maximum 1000000000
- Point 1 y — minimum -1000000000; maximum 1000000000
- Point 2 x — minimum -1000000000; maximum 1000000000
- Point 2 y — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Point 1 x | 1 |
| Point 1 y | 2 |
| Point 2 x | 5 |
| Point 2 y | 10 |
Rise = 8; run = 4; slope = 2; angle ≈63.4349°; y-intercept = 0.
Assumptions and limits
- The two points are finite Cartesian coordinates in one flat coordinate system.
- The points must be distinct so that they define one line.
- A vertical line has zero run and therefore an undefined finite slope and no y-intercept form.
- The direction angle is measured from the positive x-axis using atan2 and may be negative for a downward ordered direction.
- The result describes a line through the two points, not a geographic bearing or a regression estimate.
- Coordinate units are assumed compatible; the slope unit is y-units per x-unit.
- Rounding is applied only to display, not to the entered point differences before calculation.
- Measurement uncertainty, line thickness, and outlier treatment are outside this two-point model.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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