Gradient Calculator
Calculate the gradient (slope) between two points with step-by-step solutions
Calculate Gradient Between Two Points
First Point (x₁, y₁)
Second Point (x₂, y₂)
Enter Coordinates
Please enter coordinates for both points to calculate the gradient.
Note: The two points must be different to calculate a valid gradient.
Example Calculation
Mountain Slope Example
Point 1: (-2, 1)
Point 2: (3, 11)
Rise: 11 - 1 = 10
Run: 3 - (-2) = 5
Gradient: 10 ÷ 5 = 2
Interpretation: For every 1 unit horizontally, the line rises 2 units
Gradient Interpretation
Positive Gradient
Line rises from left to right
Negative Gradient
Line falls from left to right
Zero Gradient
Horizontal line (flat)
Undefined Gradient
Vertical line
Quick Tips
Gradient = rise ÷ run = (y₂ - y₁) ÷ (x₂ - x₁)
A 1/10 gradient means 1 unit rise per 10 units run
Percentage gradient = gradient × 100%
Gradient and slope are the same thing
Understanding Gradient
What is Gradient?
The gradient (also called slope) is a mathematical measure of how steep a line is. It tells us how much the line rises or falls for each unit of horizontal distance. Think of it as the "steepness" of a mountain or hill.
Gradient Formula
Gradient = rise ÷ run = (y₂ - y₁) ÷ (x₂ - x₁)
- Rise: Vertical change (y₂ - y₁)
- Run: Horizontal change (x₂ - x₁)
- Points: (x₁, y₁) and (x₂, y₂)
Real-world Applications
- •Construction: Roof pitch and ramp design
- •Transportation: Road and railway grades
- •Sports: Ski slope difficulty ratings
- •Engineering: Drainage and water flow
- •Economics: Rate of change in graphs
Tip: A gradient of 0.1 (or 10%) means the line rises 1 unit for every 10 units horizontally.
Common Gradient Values
Gentle Slopes
0% to 5% (0 to 0.05)
Sidewalks, driveways
Moderate Slopes
5% to 15% (0.05 to 0.15)
Residential roads
Steep Slopes
15%+ (0.15+)
Mountain roads, ski slopes