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Calculate slope, gradient, angle & equation of line between two points instantly. Get accurate results with step-by-step solutions.
Find slope, angle & equation between two points
Slope Formula: m = (y₂ - y₁) / (x₂ - x₁)
Enter coordinates of two points to calculate slope, angle, and line equations
A slope calculator is a mathematical tool that calculates the steepness and direction of a line between two points on a coordinate plane. The slope (also called gradient) represents the rate of change and is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
Enter Point 1: Input the x and y coordinates of the first point (x₁, y₁)
Enter Point 2: Input the x and y coordinates of the second point (x₂, y₂)
Calculate: Click the "Calculate Slope" button to get instant results
View Results: See slope value, angle, equations, and complete step-by-step solution
The basic slope formula calculates the ratio of vertical change to horizontal change:
Example: Points (2, 3) and (5, 9) → m = (9-3)/(5-2) = 6/3 = 2
Equation of a line using one point and slope:
Used when you know slope and one point on the line
Most common form showing slope and y-intercept:
Where m = slope and b = y-intercept (where line crosses y-axis)
Visual method for finding slope:
Rise: Vertical change (up/down) = Δy = y₂ - y₁
Run: Horizontal change (left/right) = Δx = x₂ - x₁
Slope: Rise ÷ Run
Note: In basic mathematics, slope and gradient are interchangeable terms. Both use the same formula: m = Δy/Δx. The choice of term often depends on geographic location or specific mathematical context.
To calculate slope between two points, use the formula m = (y₂ - y₁) / (x₂ - x₁). First, subtract the y-coordinates to find the rise, then subtract the x-coordinates to find the run, and finally divide rise by run. For example, given points (2,3) and (5,9): rise = 9-3 = 6, run = 5-2 = 3, so slope m = 6/3 = 2.
The slope formula is m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two distinct points on a line. This formula calculates the rate of change by dividing the vertical change (rise) by the horizontal change (run), giving you the steepness and direction of the line.
In mathematics, slope represents the steepness and direction of a line on a coordinate plane. It is calculated as the ratio of vertical change (rise) to horizontal change (run) between any two points on the line. A positive slope indicates the line rises from left to right, while a negative slope means it falls. Zero slope represents a horizontal line, and undefined slope represents a vertical line.
To find slope from two coordinates, apply the formula m = (y₂ - y₁) / (x₂ - x₁). Identify your two points with their x and y values, subtract the second y-value from the first, subtract the second x-value from the first, then divide the y-difference by the x-difference. The resulting number is your slope value.
Rise over run is a method to calculate slope where "rise" represents the vertical change (Δy = y₂ - y₁) and "run" represents the horizontal change (Δx = x₂ - x₁). The slope equals rise divided by run: m = rise/run = Δy/Δx. This visual approach helps understand how steep a line is by comparing vertical movement to horizontal movement.
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