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Angle Calculation Formula:
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The slope ratio to angle conversion calculates the angle of inclination from the ratio of vertical rise to horizontal run. This is fundamental in trigonometry, construction, engineering, and various scientific applications.
The calculator uses the trigonometric formula:
Where:
Explanation: The arctangent function calculates the angle whose tangent equals the rise/run ratio, then converts from radians to degrees for practical use.
Details: Accurate angle calculation is essential for roof pitch determination, road grading, wheelchair ramp design, staircase construction, and various engineering applications where slope measurement is critical.
Tips: Enter rise and run values as unitless ratios (e.g., 3:12 slope would be rise=3, run=12). Both values must be positive, with run greater than zero.
Q1: What is the difference between slope ratio and angle?
A: Slope ratio expresses steepness as a ratio (rise:run), while angle expresses it in degrees from horizontal.
Q2: What is a common slope ratio for roofs?
A: Residential roofs typically range from 4:12 (18.4°) to 12:12 (45°), with 4:12 being the minimum for most shingle applications.
Q3: How accurate is this calculation?
A: The calculation is mathematically precise, limited only by the precision of your input values and the computational accuracy.
Q4: Can I use this for percent grade calculations?
A: Percent grade = (rise/run) × 100. This calculator gives you the angle, which is different from percent grade.
Q5: What's the maximum angle this calculator can handle?
A: Theoretically up to 90°, but practically limited by the rise/run ratio. As run approaches zero, the angle approaches 90°.