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Slope = tan(Gradient):
| From: | To: |
The Gradient To Slope calculation converts an angle in radians to its corresponding slope value using the tangent trigonometric function. This is particularly useful in mathematics, engineering, and physics applications where angle measurements need to be converted to slope ratios.
The calculator uses the simple trigonometric formula:
Where:
Explanation: The tangent of an angle in a right triangle represents the ratio of the opposite side to the adjacent side, which is exactly the definition of slope.
Details: Slope calculation is fundamental in various fields including civil engineering for road design, architecture for roof pitch determination, mathematics for derivative calculations, and physics for analyzing inclined planes.
Tips: Enter the gradient value in radians. The calculator will compute the corresponding slope using the tangent function. Note that for angles approaching π/2 radians (90 degrees), the slope approaches infinity.
Q1: What's the difference between gradient and slope?
A: In mathematics, gradient often refers to the angle measurement (in radians or degrees), while slope refers to the ratio of vertical change to horizontal change (rise over run).
Q2: Can I input degrees instead of radians?
A: This calculator specifically requires radians. To convert degrees to radians, multiply by π/180 before entering the value.
Q3: What does a slope of 1 mean?
A: A slope of 1 means a 45-degree angle (π/4 radians), where the vertical and horizontal distances are equal.
Q4: Why does the calculator use radians instead of degrees?
A: Radians are the standard unit of angular measurement in advanced mathematics and most programming languages, including those used in Desmos.
Q5: What are the limitations of this calculation?
A: The tangent function is undefined at π/2 radians (90 degrees) and produces increasingly large values as the angle approaches this value from either side.