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Slope to Angle Formula:
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The slope to angle formula converts the slope of a line (m) to the angle (θ) that the line makes with the positive x-axis. This mathematical relationship is fundamental in trigonometry, geometry, and various engineering applications.
The calculator uses the inverse tangent function:
Where:
Explanation: The arctangent function returns the angle whose tangent equals the given slope value. The result can be expressed in degrees or radians.
Details: This conversion is essential in civil engineering for road gradients, in physics for projectile motion analysis, in computer graphics for line rendering, and in navigation for calculating bearings and inclines.
Tips: Enter the slope value (can be positive, negative, or zero), select your preferred angle unit (degrees or radians), and click calculate. The slope represents the ratio of vertical change to horizontal change.
Q1: What does a negative slope indicate?
A: A negative slope indicates the line is decreasing (falling from left to right), resulting in a negative angle measured clockwise from the positive x-axis.
Q2: What is the range of angles produced?
A: The arctan function typically returns angles between -90° and +90° (-π/2 to +π/2 radians), covering all possible line orientations except vertical lines.
Q3: How do I handle vertical lines?
A: Vertical lines have undefined slope. Their angle is 90° or π/2 radians from the positive x-axis, but this calculator cannot compute it directly from slope.
Q4: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 units, while radians use 2π units. Radians are more natural for mathematical calculations, while degrees are more intuitive for everyday use.
Q5: Can I use this for 3D slopes?
A: This calculator is for 2D lines. For 3D surfaces, you would need to calculate angles relative to multiple planes using more complex trigonometric functions.