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Angle Calculation Formula:
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The angle from slope calculation converts the slope of a line (rise over run) into an angle measured in degrees. This is commonly used in geometry, trigonometry, engineering, and construction to determine the inclination of surfaces.
The calculator uses the trigonometric formula:
Where:
Explanation: The arctangent function converts the slope ratio into an angle in radians, which is then converted to degrees using the 180/π conversion factor.
Details: Calculating angles from slopes is essential in various fields including civil engineering for ramp design, architecture for roof pitches, mathematics for line analysis, and physics for inclined plane problems.
Tips: Enter the slope value as a decimal (e.g., 0.5 for 1:2 slope, 1.0 for 45° angle). Positive values indicate upward slopes, negative values indicate downward slopes.
Q1: What is the relationship between slope and angle?
A: Slope is the tangent of the angle. A slope of 1 corresponds to 45°, while slopes less than 1 produce smaller angles and slopes greater than 1 produce larger angles.
Q2: What is the range of possible angles?
A: The angle can range from -90° to +90° (-90° for vertical downward, +90° for vertical upward).
Q3: How do I calculate slope from rise and run?
A: Slope = rise ÷ run. For example, if a ramp rises 3 meters over 12 meters, the slope is 3/12 = 0.25.
Q4: What about percentage grade?
A: Percentage grade = slope × 100%. A 10% grade means the slope is 0.10, which corresponds to approximately 5.71°.
Q5: Are there limitations to this calculation?
A: This calculation assumes a straight line and works for all real slope values. For vertical lines (infinite slope), the angle is 90° and requires special handling.