Calculate the slope of a line between two points instantly with our free online slope calculator. Perfect for algebra homework, geometry problems, and any task requiring slope calculations.
Enter two points to find the slope of the line between them:
Copy the code below to embed this calculator on your website
Getting your answer is straightforward. You just need the coordinates of two distinct points on the line.
The number our slope of a line calculator provides is more than just an answer; it describes the direction and steepness of the line.
A positive slope means the line moves uphill as you look at it from left to right. The larger the positive number, the steeper the line. For example, a line with a slope of 5 is much steeper than a line with a slope of 0.5. A real-world context could be a company's revenue chart showing a positive slope, which indicates growth over time.
A negative slope means the line moves downhill from left to right. The larger the absolute value of the negative number, the steeper the descent. For example, a line with a slope of -4 is steeper than a line with a slope of -1. A real-world context could be a graph showing the remaining fuel in a car over a journey, which would have a negative slope.
A zero slope indicates a perfectly horizontal line. There is no vertical change as you move along the line; the 'rise' is zero. For example, the line passes through points (2, 5) and (8, 5). A real-world context could be a graph of the altitude of a car driving on a perfectly flat road.
An undefined slope describes a perfectly vertical line. There is no horizontal change as you move along the line; the 'run' is zero. Division by zero is mathematically undefined, hence the name. For example, the line passes through points (3, 2) and (3, 9). A real-world context could be a graph representing a ball dropped straight down from a building at a single moment in time.
At its core, slope is the ratio of the vertical change to the horizontal change between any two points on a line. This is often remembered by the phrase 'rise over run.' The formula used by our slope calculator is a cornerstone of algebra and geometry. The formula for the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
This formula is also expressed as Rise/Run or Δy/Δx.
Let's break down each component:
While our slope calculator is the fastest method, it's essential to know how to perform the calculation manually. Let's work through an example.
Step 1: Identify your coordinates. Point 1: (x₁, y₁) = (3, 4), Point 2: (x₂, y₂) = (7, 12).
The concept of slope transcends the classroom. It's a practical tool used across numerous professional fields to measure and interpret rates of change.
While incredibly useful, the standard slope formula has one primary limitation: it only applies to straight lines in a two-dimensional plane. For a curved line, the 'steepness' is constantly changing. To find the slope at a specific point on a curve, you need to use differential calculus to find the derivative, which gives you the slope of the tangent line at that exact point. Our slope of a line calculator is designed for the linear relationships found in algebra and geometry.
In the context of two-dimensional coordinate geometry, the terms slope and gradient are used interchangeably. They both refer to the same concept of a line's steepness. 'Gradient' is more commonly used in the UK and in higher-level mathematics and sciences (e.g., 'temperature gradient').
An undefined slope occurs with a vertical line. This happens when the two points on the line have the same x-coordinate (e.g., (5, 2) and (5, 10)). When you plug this into the formula, the denominator (x₂ - x₁) becomes zero (5 - 5 = 0). Since division by zero is mathematically undefined, we say the slope is undefined.
Absolutely. A slope can be any real number. A fractional slope like 2/3 simply means that for every 3 units you move horizontally (the run), you move 2 units vertically (the rise). This is very common in real-world applications like calculating the pitch of a roof.
Slope (m) is a critical component of a line's equation. The most common form is the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. If you have the slope and a single point, you can determine the line's full equation.
Understanding slope is fundamental to mastering linear relationships in mathematics. Whether you're working on algebra homework, analyzing data trends, or solving real-world problems, our Slope Calculator provides the precision and speed you need.
Ready to explore more algebraic concepts? Check out our Parabola Calculator to work with quadratic functions, or use our Standard Form to Slope Intercept Calculator to convert between different equation forms.
Calculate parabola properties including vertex, focus, directrix, and axis of symmetry.
AlgebraSolve the classic diamond problem to find two numbers from their sum and product.
AlgebraSolve proportions and ratios instantly using cross multiplication method.
AlgebraConvert linear equations from standard form to slope-intercept form instantly.
AlgebraGet instant results with our optimized calculation engine
Precise calculations you can trust for any project
Works perfectly on all devices and screen sizes