ganak.appSlope Calculator
Calculate slope from two points, find angle of incline, percentage grade, and line equations in slope-intercept, point-slope, and standard form. Convert between slope, degrees, and percent grade. Interactive graph with step-by-step solutions, distance, midpoint, and parallel/perpendicular slopes.
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