Rise Over Run Calculator
Enter any two points on a line and this calculator finds the rise (vertical change), the run (horizontal change), the slope as a fraction and a decimal, the equivalent percent grade, the angle in degrees, and the straight-line distance between the points. Switch to Slope mode to enter a known slope and one coordinate to find the missing point.
Formula
Worked example
Points (1, 2) and (5, 6): rise = 6 - 2 = 4, run = 5 - 1 = 4, slope = 4/4 = 1.0, grade = 100%, angle = arctan(1) = 45 degrees, distance = sqrt(4^2 + 4^2) = sqrt(32) = 5.657 units.
What is rise over run?
Rise over run is the most intuitive way to describe the steepness of a straight line. The rise is the vertical change between two points (how far you move up or down), and the run is the horizontal change (how far you move left or right). Dividing rise by run gives the slope, which is the single number that completely describes how steep or flat the line is. A slope of 2 means the line goes up 2 units for every 1 unit of horizontal travel. A slope of -0.5 means it falls half a unit for every unit of horizontal travel. A slope of 0 means the line is perfectly horizontal. When the run is zero, the slope is undefined because the line is vertical.
How to calculate slope from two points
Label the first point (x1, y1) and the second point (x2, y2). Compute the rise as y2 minus y1 and the run as x2 minus x1, then divide: slope = (y2 - y1) / (x2 - x1). The order of the points does not matter because reversing them negates both numerator and denominator, leaving the ratio unchanged. Once you have the slope and either point, the y-intercept follows from b = y1 - m * x1, and the full slope-intercept equation of the line is y = mx + b. The percent grade is slope times 100 - so a slope of 0.05 equals a 5% grade, the maximum permitted for ADA wheelchair ramps. The angle with the horizontal is the inverse tangent of the absolute value of the slope, expressed in degrees.
Real-world uses of rise over run
Rise over run appears whenever a rate of change must be described. In construction, roof pitch is expressed as the rise in inches per 12 inches of horizontal run (a 4:12 pitch has a slope of 4/12 = 0.333). Road engineers specify grades as percentages: a 6% grade rises 6 feet for every 100 feet of horizontal distance, which is near the upper limit considered safe for highway driving. ADA accessibility standards require ramps to have a maximum slope of 1:20, or 5%. In algebra, slope is the m in y = mx + b and describes how quickly the dependent variable changes with the independent variable. In physics, slope on a position-time graph is velocity, and slope on a velocity-time graph is acceleration. In data analysis, the slope of a regression line quantifies the relationship between two variables.
Positive, negative, zero and undefined slopes
A positive slope means the line rises from left to right: as x increases, y increases. A negative slope means the line falls from left to right: as x increases, y decreases. A zero slope is a horizontal line where y never changes no matter how x changes, described simply as y = b. An undefined slope belongs to a vertical line where x never changes; it cannot be written in slope-intercept form and is instead described as x = a. Understanding the sign and magnitude of a slope immediately tells you the direction and steepness of the line without having to plot any points.
Slope and grade reference
| Grade (%) | Slope (m) | Angle (°) | Typical use |
|---|---|---|---|
| 0% | 0 | 0° | Level floor or road |
| 2% | 0.02 | 1.1° | Minimum drainage slope |
| 5% | 0.05 | 2.9° | ADA wheelchair ramp (max permitted) |
| 8.3% | 0.083 | 4.7° | Maximum parking ramp for accessibility |
| 10% | 0.10 | 5.7° | Steep driveway |
| 12% | 0.12 | 6.8° | Steep road grade |
| 25% | 0.25 | 14.0° | Ski slope (blue/intermediate) |
| 45% | 0.45 | 24.2° | Ski slope (black diamond) |
| 100% | 1.00 | 45° | 1:1 slope, 45-degree angle |
Common grade ranges and their typical real-world applications. Grade = slope expressed as a percentage.
Frequently asked questions
What is the rise over run formula?
The formula is slope = rise / run = (y2 - y1) / (x2 - x1). Rise is the vertical change between the two points and run is the horizontal change. Divide the rise by the run to get the slope. For example, if the first point is (2, 3) and the second is (8, 9), rise = 9 - 3 = 6 and run = 8 - 2 = 6, so slope = 6/6 = 1.
What does a negative slope mean?
A negative slope means the line falls as you move from left to right. The rise is negative while the run is positive (or vice versa), so their ratio is negative. For example, a slope of -2 means the line drops 2 units for every 1 unit of horizontal movement.
How do I convert slope to percent grade?
Multiply the slope by 100. A slope of 0.06 equals a 6% grade. Percent grade is commonly used for road inclines, drainage plans and accessibility ramp specifications. A 5% grade (slope = 0.05) is the steepest wheelchair ramp allowed under ADA guidelines.
How do I convert slope to angle in degrees?
Use the arctangent: angle = arctan(|slope|) converted from radians to degrees. Most scientific calculators have an atan or tan-1 button. For a slope of 1, the angle is arctan(1) = 45 degrees. For a slope of 0.5, the angle is approximately 26.6 degrees.
What happens when the run is zero?
When the run is zero, the slope is undefined because you would be dividing by zero. This corresponds to a vertical line, which has infinite steepness. Vertical lines are described by the equation x = a constant, not by slope-intercept form.
How do I find rise and run from the slope alone?
Any slope can be written as a fraction. For example, a slope of 0.75 = 3/4, so the rise is 3 and the run is 4 (or any multiple, such as rise = 6, run = 8). Use the rise-and-run mode in this calculator to enter any rise and run and see the corresponding slope and angle.