Methodology
How this calculator works
For points (x₁,y₁) and (x₂,y₂), slope m = (y₂ − y₁) ÷ (x₂ − x₁). The line uses y = mx + b, where b = y₁ − mx₁. Distance and midpoint are calculated from the same coordinate changes.
Formula testedGeometry & Coordinate Math
Slope Calculator
Find the slope between two points and inspect rise, run, angle, grade, intercepts, distance, midpoint and the resulting straight-line equation.
Geometry & coordinate math
Find slope and the complete line
Enter two points to calculate rise, run, slope, angle, percentage grade, distance, midpoint, intercepts and the line equation.
Your entries stay in this browser and are used only for this calculation.
Line result
Enter your values
Slope, line equation and coordinate details will appear here.
Worked example
Reading the result
For (1,2) and (5,10), rise is 8 and run is 4, so slope is 2. The line is y = 2x, the grade is 200%, and the distance is √80 ≈ 8.944.
Interpret the result
Slope is a signed rate of change
Positive, negative, zero and undefined slopes describe increasing, decreasing, horizontal and vertical lines. The angle and grade express the same relationship in forms used by geometry, engineering and construction.
Reference formula
Rise divided by run
OpenStax defines slope as vertical change divided by horizontal change and illustrates the right-triangle interpretation used here.
OpenStax: slope of a lineRelated geometry tools
Continue solving
Common questions
Frequently asked questions
How do I find slope from two points?+
Subtract the first y-coordinate from the second to get rise, subtract the first x-coordinate from the second to get run, then divide rise by run.
Why is a vertical line's slope undefined?+
A vertical line has zero horizontal change. Dividing its rise by a run of zero is undefined, so its equation is written x = constant.
What does a negative slope mean?+
A negative slope means y decreases as x increases. The line falls from left to right.
Is percentage grade the same as slope?+
Grade is slope multiplied by 100. A slope of 0.08 corresponds to an 8% grade.
How is the line angle calculated?+
The calculator applies the inverse tangent to the slope and normalizes the inclination to the range from 0° up to 180°.
Does swapping the two points change the answer?+
No. Rise and run both reverse sign, so their ratio, the line and the distance remain the same.
Important scope
The result describes the infinite straight line through the two entered points. Real-world road, roof and terrain measurements may require horizontal projected run rather than surface distance. This calculator is for planning and education, not personal financial advice.