Rise Over Run Calculator

How to Calculate Rise Over Run

Rise over run is a method used to calculate the slope of a line or the steepness of an incline. It's a fundamental concept in geometry and trigonometry, often used in various real-world applications such as construction, engineering, and physics.

Rise Over Run Formula

The rise over run formula, also known as the slope formula, is:

\[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

• Rise is the vertical change (change in y-coordinates)
• Run is the horizontal change (change in x-coordinates)
• (x₁, y₁) and (x₂, y₂) are two points on the line

Calculation Steps

1. Identify two points on the line or the rise and run values
2. If using points:
   • Calculate the rise: y₂ - y₁
   • Calculate the run: x₂ - x₁
3. Divide the rise by the run to get the slope

Example Calculation

Let's calculate the slope of a line passing through the points (1, 2) and (4, 6).

1. Identify the points:
   (x₁, y₁) = (1, 2)
   (x₂, y₂) = (4, 6)
2. Calculate the rise: \[ \text{Rise} = y_2 - y_1 = 6 - 2 = 4 \]
3. Calculate the run: \[ \text{Run} = x_2 - x_1 = 4 - 1 = 3 \]
4. Calculate the slope: \[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{4}{3} \approx 1.33 \]

Visual Representation

A visual representation can help understand the concept better. Here's a diagram showing the rise and run for the example above:

This diagram illustrates the rise (vertical change) and run (horizontal change) between the two points, which are used to calculate the slope.