Permille Per Mile Calculator

Permille Per Mile Formula:

\[ \text{Permille Per Mile} = \frac{\text{Rise}}{\text{Run}} \times 1000 \]

Permille Per Mile:

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1. What Is Permille Per Mile?

Permille per mile (‰/mile) is a unit of measurement that expresses slope or gradient. It represents the vertical rise in meters per 1000 units (mile) of horizontal distance. This measurement is commonly used in transportation engineering, road design, and railway construction to describe grades and inclines.

2. How Does The Calculator Work?

The calculator uses the permille per mile formula:

\[ \text{Permille Per Mile} = \frac{\text{Rise}}{\text{Run}} \times 1000 \]

Where:

\( Rise \) — Vertical height difference (meters)
\( Run \) — Horizontal distance (miles)
\( 1000 \) — Conversion factor to express as permille

Explanation: The formula calculates how many meters of vertical change occur per 1000 units of horizontal distance, providing a standardized way to express slopes over longer distances.

3. Applications Of Slope Measurement

Details: Permille per mile measurements are crucial in transportation planning, helping engineers design roads and railways with appropriate grades for safety and efficiency. They're also used in land surveying, construction projects, and environmental studies where precise slope measurements are required over extended distances.

4. Using The Calculator

Tips: Enter the vertical rise in meters and the horizontal run in miles. Both values must be positive numbers, with run greater than zero. The calculator will compute the slope expressed as permille per mile (‰/mile).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between percent grade and permille?
A: Percent grade expresses slope as rise per 100 units of run, while permille expresses it as rise per 1000 units of run. Permille provides finer resolution for gentle slopes.

Q2: Why use miles instead of kilometers?
A: This calculator uses miles as it's designed for regions using imperial measurements. For metric calculations, use meters of rise per kilometer of run.

Q3: What is considered a steep slope in permille per mile?
A: In transportation, slopes above 50-70 ‰/mile are generally considered steep and may require special engineering considerations.

Q4: Can I use this for very short distances?
A: While technically possible, permille per mile is most meaningful for longer distances where the measurement scale is appropriate.

Q5: How does this relate to angle measurement?
A: Permille per mile can be converted to degrees using trigonometric functions, but it's often more practical for engineering applications to work directly with the linear measurement.