Slope Calculator
Calculate the slope (gradient) of a line using points or angle. Get instant results including distance and angle of inclination.
Slope (m):
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Angle of Inclination:
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Distance:
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Line Equation:
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Understanding Slope and Gradient
The slope (or gradient) of a line is a measure of its steepness and direction. It represents the rate of change between two points and is a fundamental concept in mathematics, engineering, and many real-world applications.
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁) = rise/run = tan(θ)
Where: m is slope, (x₁,y₁) and (x₂,y₂) are points on the line, θ is the angle of inclination
How to Calculate Slope
- Identify two points on the line (x₁,y₁) and (x₂,y₂)
- Calculate the change in y (rise): Δy = y₂ - y₁
- Calculate the change in x (run): Δx = x₂ - x₁
- Divide rise by run: slope = Δy/Δx
- The angle can be found using: θ = arctan(slope)
Types of Slopes
- Positive Slope (m > 0): Line goes upward from left to right
- Negative Slope (m < 0): Line goes downward from left to right
- Zero Slope (m = 0): Horizontal line
- Undefined Slope: Vertical line
Applications of Slope
Slope calculations are crucial in many fields:
- Civil Engineering: Road and ramp design, drainage systems
- Architecture: Roof pitch, staircase design
- Physics: Motion analysis, force vectors
- Economics: Rate of change, trend analysis
- Geography: Terrain analysis, topographic mapping