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Slope to Degrees Formula:
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The slope to degrees conversion calculates the angle of inclination from a given slope ratio. This is commonly used in mathematics, engineering, construction, and various scientific applications to determine the steepness of surfaces.
The calculator uses the trigonometric formula:
Where:
Explanation: The arctangent function converts the slope ratio (a dimensionless number) into an angle measured in degrees, representing the angle between the inclined surface and the horizontal plane.
Details: Calculating slope angles is essential for construction projects, road design, roof pitch determination, wheelchair ramp design, and various engineering applications where precise angle measurements are required for safety and functionality.
Tips: Enter the slope value as a unitless ratio (rise divided by run). For example, a slope of 1:2 would be entered as 0.5, and a slope of 3:1 would be entered as 3. The calculator will return the corresponding angle in degrees.
Q1: What is the difference between slope and angle?
A: Slope is expressed as a ratio (rise:run or rise/run), while angle is measured in degrees and represents the actual inclination relative to horizontal.
Q2: What does a slope of 1 mean in degrees?
A: A slope of 1 (45° angle) represents equal rise and run, creating a perfect diagonal line.
Q3: How do I convert degrees back to slope?
A: Use the tangent function: slope = tan(angle_in_degrees). Multiply the result by 100 to get percentage grade.
Q4: What are common slope angles in construction?
A: Common angles include: wheelchair ramps (4.76° for 1:12 slope), standard stairs (30-40°), roof pitches (14-45° depending on design).
Q5: Can this calculator handle negative slopes?
A: Yes, negative slopes will return negative angles, representing downward inclinations from the horizontal reference.