Rise Over Run Calculator
Calculate slope, rise, run, and line properties from two points
Calculate Rise Over Run
First point: (0, 0)
Second point: (0, 0)
Rise Over Run Results
Please enter two different points to calculate rise over run.
Example Calculation
Example: Roof Slope
Point 1: (0, 0) - Base of roof
Point 2: (12, 4) - End of roof (12 feet horizontal, 4 feet vertical)
Rise: 4 - 0 = 4 feet
Run: 12 - 0 = 12 feet
Slope: 4/12 = 0.3333 or 1:3 ratio
Percentage Grade: 33.33% (common roof slope)
Types of Slopes
Positive Slope
Line rises from left to right
m > 0
Negative Slope
Line falls from left to right
m < 0
Zero Slope
Horizontal line
m = 0
Undefined Slope
Vertical line
Division by zero
Slope Tips
Rise = vertical change (Δy)
Run = horizontal change (Δx)
Slope = rise ÷ run = Δy/Δx
Order of points doesn't matter for slope
Percentage grade = slope × 100%
Understanding Rise Over Run
What is Rise Over Run?
Rise over run is a method for calculating the slope of a line between two points. It represents how much the line goes up (or down) for every unit it goes to the right.
Key Concepts
- •Rise: Vertical change between points (Δy = y₂ - y₁)
- •Run: Horizontal change between points (Δx = x₂ - x₁)
- •Slope: Rise divided by run (m = Δy/Δx)
Formula
m = (y₂ - y₁) / (x₂ - x₁)
- m: Slope of the line
- (x₁, y₁): First point coordinates
- (x₂, y₂): Second point coordinates
Special Case: When x₂ = x₁ (vertical line), the slope is undefined because we divide by zero.
Real-World Applications
Construction
Calculating roof pitch, stair slopes, and ramp angles for accessibility compliance.
Engineering
Designing roads, railways, and drainage systems with proper gradients.
Economics
Analyzing trends in data, such as cost changes over time or growth rates.