ganak.appSlope Calculator
Calculate slope from two points, find angle, percentage grade, and line equations. Interactive graph with step-by-step solutions, distance, and midpoint.
Interactive Graph
Visualize the line with points and intercepts
Slope Details
Multiple representations of the slope value
Line Equations
Three standard forms of the line equation
Distance & Midpoint
Measurements between and around the points
Parallel & Perpendicular
Related lines with same or negative reciprocal slopes
Step-by-Step Solution
Formula, substitution, and result for each solving step
Identify the points
P₁(x₁, y₁) and P₂(x₂, y₂)
P₁(2, 3) and P₂(6, 7)
Calculate rise (change in y)
rise = y₂ − y₁
rise = 7 − 3
rise = 4
Calculate run (change in x)
run = x₂ − x₁
run = 6 − 2
run = 4
Calculate slope
m = rise ÷ run
m = 4 ÷ 4
m = 1
Calculate angle of incline
θ = arctan(|m|)
θ = arctan(1)
θ = 45°
How to Calculate Slope
The rise over run formula explained step by step
The slope of a line measures its steepness and direction. It tells you how much the line rises or falls for each unit of horizontal movement. Slope is represented by the letter m and is calculated as the ratio of vertical change (rise) to horizontal change (run) between any two points on the line.
Slope Formula
m = (y₂ − y₁) / (x₂ − x₁) = rise / run
A positive slope means the line rises from left to right. A negative slope means it falls. A slope of zero is a perfectly horizontal line, while an undefined slope indicates a vertical line.
Slope Formulas & Equation Forms
Key formulas for representing lines
Slope Formula
m = (y₂ − y₁) / (x₂ − x₁)
Calculates slope from two coordinate points
Slope-Intercept Form
y = mx + b
Where m is slope and b is y-intercept
Point-Slope Form
y − y₁ = m(x − x₁)
Useful when you know one point and the slope
Standard Form
Ax + By = C
Integer coefficients with A > 0
Types of Slope
Understanding positive, negative, zero, and undefined slopes
Positive Slope
Line rises from left to right (m > 0). Example: a hill going upward. The larger the value, the steeper the incline.
Negative Slope
Line falls from left to right (m < 0). Example: a ski slope going downhill. The more negative, the steeper the descent.
Zero Slope
Perfectly horizontal line (m = 0). There is no rise — the line stays at the same y-value. Example: a flat road.
Undefined Slope
Vertical line where run = 0. Division by zero makes slope undefined. Equation is x = c. Example: a wall or cliff.
Real-World Applications
Where slope calculations matter in everyday life
Construction & Roofing
Roof pitch is expressed as rise/run (e.g., 4/12 pitch). Drainage systems require minimum slopes to ensure water flow.
Roads & Transportation
Road grades are measured as percentage slope. Highways typically max out at 6% grade; mountain roads may reach 8-12%.
ADA Accessibility
Wheelchair ramps must not exceed 1:12 slope (8.33% grade or 4.76 degrees). Landings are required every 30 feet of run.
Mathematics & Science
Slope represents rate of change in physics, economics, and statistics. Linear regression finds the best-fit slope through data points.
Frequently Asked Questions
Common questions about slope calculations
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Last updated Mar 2, 2026