The Angle and Pitch Calculator on freeonlinecalculators.net is a versatile tool designed to simplify the process of determining angles, pitch, and slopes for various applications. Whether you’re a construction professional, an engineer, or a DIY enthusiast, this calculator helps you quickly convert pitch to angle, slope, or grade, and vice versa.
Roof Pitch Calculator
Calculate the roof pitch (angle) using the formula:
\[
\theta = \arctan\left(\frac{\text{Rise}}{\text{Run}}\right)
\]
and convert it to degrees.
* Enter the roof rise and run (in meters).
Step 1: Enter Roof Dimensions
Example: 3 m
Example: 12 m
Angle and Pitch Calculator - Educational Guide
Understanding the angle of elevation and pitch (slope) is crucial for many construction, engineering, and DIY projects. While our Angle and Pitch Calculator makes these calculations effortless, this guide explains how to manually compute these values for those who want to understand the process or verify results.
1. Angle of Elevation
The angle of elevation is the angle between a horizontal line and the line of sight looking upward to an object.
Formula to Calculate the Angle of Elevation
θ = arctan(rise / run)
- θ (theta) is the angle of elevation in degrees.
- rise is the vertical distance (height).
- run is the horizontal distance (length).
Example:
If the height of a hill is 10 meters (rise) and the horizontal distance (run) is 30 meters, the angle of elevation is calculated as:
θ = arctan(10 / 30) = arctan(0.333) ≈ 18.43°
2. Pitch (Slope)
Pitch refers to the slope of a surface and is typically expressed as a percentage or in degrees.
Formula to Calculate Pitch as a Percentage
Pitch (%) = (rise / run) × 100
Formula to Calculate Pitch in Degrees
Pitch (degrees) = arctan(rise / run)
Example:
If you have a rise of 10 meters and a run of 30 meters, the pitch in percentage and degrees can be calculated as follows:
Pitch (%) = (10 / 30) × 100 = 33.33%
Pitch (degrees) = arctan(10 / 30) ≈ 18.43°
Key Steps for Manual Calculation
- 1. Measure the rise (vertical distance).
- 2. Measure the run (horizontal distance).
- 3. Use the formulas above to calculate either the angle or pitch.
This guide provides the basic formulas you need to calculate the angle of elevation and pitch manually. You can use a scientific calculator to perform the arctan (inverse tangent) operation for accurate results.