Slope Calculator
Calculate the slope, distance, and angle between two points instantly. Find the equation of the line and percent grade with this coordinate geometry tool.
1Point 1 (x₁, y₁)
2Point 2 (x₂, y₂)
Slope Formula
The slope ($m$) represents the steepness and direction of a line. It is calculated by dividing the change in height ($\Delta y$) by the change in horizontal distance ($\Delta x$).
m = (y₂ - y₁) / (x₂ - x₁)
- Positive Slope: The line goes up from left to right.
- Negative Slope: The line goes down from left to right.
- Zero Slope: A horizontal line.
- Undefined Slope: A vertical line (division by zero).
Percent Grade
In construction and engineering, slope is often expressed as a percentage called "grade".
Grade = Slope × 100
For example, a slope of 0.5 is a 50% grade. A 100% grade corresponds to a 45-degree angle (slope of 1).
Distance Formula
The distance ($d$) between the two points is calculated using the Pythagorean theorem:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
? Frequently Asked Questions
The slope of a vertical line is undefined because the change in x (run) is zero, and you cannot divide by zero.
Once you have the slope (m), you can plug one of your points into the equation y = mx + b and solve for b. The calculator does this automatically.
A negative slope indicates that the line descends as you move from left to right. For example, going downhill.