Math & Engineering
Slope Calculator
Calculate the slope (gradient) between two points on a line
Reviewed by the calculator.uk.com Team · Last reviewed 21 August 2026 · Our methodology
Enter coordinates to calculate the slope
Related to Slope Calculator
The slope calculator determines the steepness or incline of a line by calculating the ratio of vertical change (rise) to horizontal change (run) between two points. This fundamental mathematical concept is expressed through the slope formula: m = (y₂ - y₁)/(x₂ - x₁), where (x₁,y₁) and (x₂,y₂) are the coordinates of two points on the line.
Key Components
The calculator provides multiple representations of slope: - Decimal form (m) - Rise over run fraction - Angle in degrees - Percent grade
The calculator also visualizes the line with an interactive graph, helping you understand the relationship between the points and the resulting slope. For vertical lines (when x₁ = x₂), the slope is undefined (infinite), and for horizontal lines (when y₁ = y₂), the slope is zero.
Understanding slope results involves interpreting several key measurements that describe the steepness and direction of a line. Each representation offers unique insights into the line's characteristics.
Slope Interpretations
- Positive Slope: Line rises from left to right
- Negative Slope: Line falls from left to right
- Zero Slope: Horizontal line
- Undefined Slope: Vertical line
The percent grade is particularly useful in real-world applications like road construction and architecture, where slope is often expressed as a percentage. For example, a slope of 0.25 converts to a 25% grade, indicating that for every 100 units of horizontal distance, there is a 25-unit change in vertical distance.
1. What is slope in mathematical terms?
Slope is a measure of steepness, calculated as the ratio of vertical change (rise) to horizontal change (run) between two points on a line. It represents the rate of change and is a fundamental concept in algebra and calculus.
2. How do I convert slope to angle?
To convert slope to angle, use the arctangent (inverse tangent) function. The angle in degrees is calculated as: angle = arctan(slope) × (180/π). Our calculator automatically performs this conversion for you.
3. What does a negative slope mean?
A negative slope indicates that the line decreases as you move from left to right. It means that for every positive change in x, there is a negative change in y. For example, a slope of -2 means that for every unit increase in x, y decreases by 2 units.
4. Why is percent grade important?
Percent grade is crucial in civil engineering, road construction, and accessibility design. It expresses slope as a percentage, making it easier to understand and communicate. For instance, a 6% grade means a 6-foot rise for every 100 feet of horizontal distance.
5. What is the scientific source for this calculator?
Slope follows directly from the definition m = (y2 - y1)/(x2 - x1) found in any algebra or calculus text such as Stewart's Calculus, with the angle derived from the arctangent of that ratio. Percent grade, a common way of expressing slope in road and accessibility design, follows the convention used by transportation engineering bodies such as AASHTO (American Association of State Highway and Transportation Officials).