Percent Grade to Degrees Calculator

Slope Angle Formula:

\[ \theta = \arctan\left(\frac{G}{100}\right) \]

Slope Angle:

degrees

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1. What is a Percent Grade to Degrees Calculator?

Definition: This calculator converts slope expressed as a percentage grade to slope angle in degrees.

Purpose: It helps engineers, surveyors, and construction professionals convert between these two common slope measurement systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \arctan\left(\frac{G}{100}\right) \]

Where:

\( \theta \) — Slope angle (degrees)
\( G \) — Percent grade (%)

Explanation: The percent grade is divided by 100 to convert to a ratio, then the arctangent function calculates the corresponding angle.

3. Importance of Slope Angle Conversion

Details: Different fields use different slope measurements - civil engineering often uses percent grade while architects typically use degrees.

4. Using the Calculator

Tips: Simply enter the percent grade value (can be positive or negative) and click calculate.

5. Frequently Asked Questions (FAQ)

Q1: What exactly is percent grade?
A: Percent grade represents the vertical rise divided by horizontal run, expressed as a percentage.

Q2: How does 100% grade relate to degrees?
A: 100% grade equals 45 degrees (arctan(1) = 45°).

Q3: What's the maximum possible percent grade?
A: Theoretically infinite (90° = ∞% grade), but practically rarely exceeds 100% in real-world applications.

Q4: When would I need this conversion?
A: When working with tools that measure in degrees (like protractors) but your specifications are in percent grade.

Q5: Can I convert degrees back to percent grade?
A: Yes, percent grade = tan(θ) × 100 where θ is in degrees.