Calculator

Free Slope Calculator Tool

Free Slope Calculator Tool

How to Calculate Slope Between Two Points with Steps

Slope Calculator – Free Online Tool with Formula, Steps & Examples

Slope Calculator

What is Slope Calculator?

A Slope Calculator is a free online tool that helps you instantly calculate the slope (or gradient) of a straight line given two points, or directly from a line equation. Slope is a measure of how steep a line is and tells you how much the line rises (vertical change) compared to how much it runs (horizontal change) between two points. Whether you're working on school maths problems, planning a ramp, studying geometry, or dealing with graphs, the slope calculator makes your work quick, visual, and accurate.

Formula or Logic Behind Slope Calculator

The slope of a straight line in coordinate geometry is calculated using this main formula:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
Here, (x₁, y₁) and (x₂, y₂) are any two different points on the line. The slope can also be determined from the line's equation:

If the equation is in the form y = mx + c, then the slope is "m".
If it is in the form Ax + By + C = 0, then slope m = -A/B.
Slope is sometimes expressed as a percentage (percent grade): Percent Slope = Slope × 100%.

Positive slope means the line goes upwards from left to right, negative means downwards, zero slope is flat, and an undefined slope means the line is vertical.

Examples: Slope Between Points and Equations

Input (Points/Equation)	Slope (m)	Working
(2, 4), (6, 12)	2	(12-4)/(6-2) = 8/4 = 2
(1, 5), (4, 11)	2	(11-5)/(4-1) = 6/3 = 2
y = 3x - 2	3	m = 3
4x + 2y = 10	-2	Slope = -A/B = -4/2 = -2
Slope grade 5%	0.05	5% = 5/100 = 0.05
1 in 100 slope	0.01	1/100 = 0.01

Steps to Use the Slope Calculator

Enter the values of x₁, y₁ and x₂, y₂ to use two points, or type a line equation.
Click on the 'Calculate' button.
Instantly see the slope value and the full solution explained below the calculator.

Why Use Vedantu’s Slope Calculator?

Vedantu’s Slope Calculator is easy to use, mobile-friendly, and designed for Indian & global students following CBSE, ICSE, and major international curricula. You'll get not just fast answers, but step-by-step working, making it perfect for learning, exam prep, construction, or quick homework checks. Trusted by millions, it's your reliable Maths tool for class 7-12 concepts and more.

Real-life Applications of Slope Calculator

Slope calculations are everywhere—not just in Maths class!

Designing roads, bridges, and railway lines to specify gradients and safety.
Building wheelchair ramps and walkways for accessibility standards.
Roof pitch planning and water drainage on buildings.
Physics and Economics: Understanding speed, velocity or graph slopes.
Graphs in statistics, finance, or any area where lines represent change.

With the Slope Calculator, all these practical needs become fast and simple.

For more maths help, explore: HCF Calculator, Prime Numbers, Polynomial, Equation of a Line, Algebra Topics

FAQs on Free Slope Calculator Tool

1. How do I calculate the slope between two points?

To calculate the slope (m) between two points (x₁, y₁) and (x₂, y₂), use the formula m = (y₂ - y₁) / (x₂ - x₁). This represents the rise (vertical change) over the run (horizontal change). Simply subtract the y-coordinates and divide by the difference in x-coordinates. Remember that a positive slope indicates an upward trend, a negative slope indicates a downward trend, a slope of zero represents a horizontal line, and an undefined slope indicates a vertical line.

2. What is the slope formula?

The most common slope formula is m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on a line. This calculates the change in y divided by the change in x, also known as 'rise over run'. Other formulas exist, such as finding the slope from the slope-intercept form of a linear equation (y = mx + b), where 'm' directly represents the slope.

3. How to find the slope of a line from its equation?

The method depends on the equation's form. For the slope-intercept form (y = mx + b), the slope is the coefficient of x, which is 'm'. For the standard form (Ax + By = C), the slope is -A/B. If the equation is in a different form, rearrange it into either slope-intercept or standard form to find the slope easily.

4. What is a 1 in 100 slope?

A 1 in 100 slope means for every 1 unit of rise (vertical change), there is a 100 unit run (horizontal change). This represents a very gentle slope. It's often expressed as a percentage (1%), representing a 1% incline.

5. What does a negative slope mean?

A negative slope indicates that as the x-value increases, the y-value decreases. Graphically, this means the line slopes downwards from left to right. The steeper the downward slope, the more negative the slope value will be.

6. What is the difference between rise over run and percent slope?

'Rise over run' is a descriptive way to express the slope as the vertical change (rise) divided by the horizontal change (run). Percent slope converts this ratio into a percentage by multiplying by 100. For example, a rise of 2 and a run of 10 is a slope of 0.2 or 20%.

7. How to calculate percent slope?

To calculate percent slope, first find the slope using the formula (y₂ - y₁) / (x₂ - x₁). Then, multiply the slope by 100 to express it as a percentage. This percentage represents the incline or decline of the line. For instance, a slope of 0.05 becomes a 5% slope.

8. What is slope used for in real life?

Slope has numerous real-world applications. It's crucial in:

Civil Engineering: Designing roads, ramps, and drainage systems.
Architecture: Determining roof pitches and building stability.
Physics: Analyzing motion and gradients in various systems.
Graphing Data: Interpreting trends and relationships between variables.

9. How to find slope from a graph?

To find the slope from a graph, select two distinct points on the line. Determine their coordinates (x₁, y₁) and (x₂, y₂). Then, apply the slope formula: m = (y₂ - y₁) / (x₂ - x₁). The result is the slope of the line represented on the graph.

10. What is a 2% slope?

A 2% slope means there's a 2-unit rise for every 100-unit run. This represents a relatively gentle incline. It's often used in contexts like road grading or ramp design to indicate a slight upward or downward slope.

11. What is the slope of a horizontal line?

The slope of a horizontal line is always zero. This is because there is no vertical change (rise) between any two points on a horizontal line; the rise is always 0, resulting in a slope of 0/run = 0.

12. What is the slope of a vertical line?

The slope of a vertical line is undefined. This is because the run (horizontal change) between any two points on a vertical line is always zero. Dividing by zero is undefined in mathematics, hence the undefined slope.