Slope Calculator: Find Slope Between Two Points

A Slope Calculator is an online tool used to find the slope of a straight line in coordinate points. The result will show how steep the line is and whether it goes up, down or flat.

Slope is a common term used in maths. It is used in Algebra, Geometry, Coordinate Geometry, Physics, Engineering, Construction and Statistics.

The slope of a line is usually denoted by the letter m. To find the slope we divide the vertical increase (rise) by the horizontal increase (run).

If a line passes through the coordinates (2,3) and (4,7), this would give us the slope of 2. As the x coordinate increases by 1 unit, the y coordinate increases by 2 units.

Our free calculator will help you calculate the slope easily. Simply put your x and y coordinates in and our tool will give you the slope of the line in seconds.

This tool is very useful to use if you’re a student in the USA learning about Algebra, Geometry and graphing equations. Especially for Standardised

Maths exams such as SAT and ACT.

Whether you’re doing your schoolwork, looking at graphs or construction measurements this online tool will help you calculate the slope.

How to Use the Slope Calculator

Using an online Slope Calculator is simple. All you need to do is insert the coordinates of two points on the straight line.

1. Insert the first set of coordinates (x1 and y1).
2. Insert the second set of coordinates (x2 and y2).
3. Ensure all of the coordinates are correct.
4. Press the calculate or solve button.
5. The result will show the slope.
6. If the calculator shows you the steps, look at the rise and run.
7. Clear the box and enter two new sets of coordinates.

Example

If our two set of coordinates are:
(2, 3) and (4, 7)

Simply put these into the calculator.

This will give us the slope of:
m=2

This means for every 1 unit moved to the right, the line rises by 2 units.

Slope Calculator Formula

The formula used to find the slope of a straight line is:

m = (y2 - y1)/(x2 - x1)
Where:
m = slope
x1 = x coordinate for the first coordinate
y1 = y coordinate for the first coordinate
x2 = x coordinate for the second coordinate
y2 = y coordinate for the second coordinate

This calculates the difference in the y coordinates and divides this by the difference in the x coordinates.

Types of Slope

There are 4 common types of slope in coordinate geometry.
Positive Slope

If there is a positive slope this means the line is going up.

Example:

m=2

Negative Slope

If there is a negative slope this means the line is going down.

Example:

m = -3

Zero Slope

If there is a zero slope this means the line is flat. Both coordinates will have the same y coordinate.

m=0

Undefined Slope

If there is an undefined slope this means the line is vertical. Both coordinates will have the same x coordinate meaning it will divide by zero.
m = (y2 - y1)/0

As you can see this cannot be done as we cannot divide by zero.

Example

Let us look at an example of how the Slope Calculator works.

Calculate the slope of a line that moves through the points (3,4) and (7, 12).

Identify the coordinates.

First set of coordinates:

(x1, y1) = (3,4)

Second set of coordinates:

(x2, y2) = (7,12)

Write out the formula for slope.

m = (y2 - y1)/(x2 - x1)
Put in the values.
m = (12 - 4)/(7 - 3)

Calculate.

m = 8/4

Final Answer:

The slope is 2. This means for every 1 unit increase in the x it will increase by 2 units vertically.

Check:

Using the slope intercept form:
y=mx+b

Plug in the first set of coordinates (3,4) and the slope (2):

4=2(3) + b
b = -2

This means the equation of the line is y = 2x - 2.

Understanding your Results

The result from your Slope Calculator will tell you how steep the straight line is between the two coordinates.

Depending on what coordinates you put in the results could mean different things. If you get a positive slope then the line goes up from left to right. If you get a negative slope then the line goes down from left to right. If you get a zero slope then the line is flat. If you get an undefined slope then the line is vertical.

If you get a fractional slope this means the line is rising or falling over a certain horizontal distance. If you get a decimal slope then this shows you the slope as a decimal. For example, if you get a slope of 0.5 this means for every 1 unit increase in the x coordinate, the line will go up 0.5 units. If you get a slope of -2 this means for every 1 unit increase in the x coordinate the line will go down 2 units vertically.

Understanding the slope can help you to understand graphs, compare how steep lines are and identify relationships in mathematical problems.

Factors Which Can Affect Your Result

There are several factors which can affect the slope.

Coordinates

The coordinates will affect the slope. If you get any of your coordinates wrong then the result will change.

Difference in Y Coordinates

The difference in y coordinates will show you the increase or decrease in the line.

Difference in X Coordinates

The difference in x coordinates will show you how much the line is running. If there is no difference (0) then the slope will be undefined.

Positive/Negative Coordinates

Your coordinates can be positive, negative or 0. Ensure you enter them correctly.

Order of Points

It doesn’t matter which order you put your points in as long as you switch both coordinates.

Decimal Numbers

If your coordinates have decimal numbers then you may get a fractional or rounded result.

Units

If your coordinates are measurements then ensure you use the same units on the axis.

Advantages of Using a Slope Calculator

There are many advantages to using an online Slope Calculator. This can help students, teachers, engineers and professionals.

Quick

The calculator will calculate the slope quickly. This means you won’t need to do any subtraction or division.

Student Friendly

Students studying Algebra, Geometry and Coordinate Graphs can use this to check their homework. This can help them practice slope problems.

Good for SAT/ACT

Understanding slope is an important part of Algebra and Coordinate Geometry questions in Standardised Maths Exams in the USA.

Graphs

Knowing the slope can help you understand the direction and steepness of the line when drawing graphs.

Construction

Professionals in construction will use slope calculations when working with ramps, roads, pipes and land.

Engineering

Engineers will use slope calculations to analyse their designs. They can see the gradient, increase in height and relationships.

Physics

Slope can be used to show the rate of change in graphs. For example, the velocity in a distance time graph or acceleration in a velocity time graph.

Business/Data

Slope can help you identify trends and relationships between variables.

Easy to Use

Most Slope Calculators on the internet can be used on desktops, laptops, tablets and smartphones.

Accuracy of Calculations

If you input the correct coordinates and they are a straight line then your calculator can give you accurate results.

However, it is important to know the following:

Ensure you input the correct coordinates. If you don’t then you will get inaccurate results.

Two Different Points

You must also ensure you have two different points. If both of your coordinates are the same then you will end up with 0/0 in the formula so it will be undefined.

Vertical Line

If the line is vertical then the slope will be undefined as there is no difference in the x coordinates.

Straight Line

The standard formula for slope is calculating the slope between two points on a straight line. If the graph is curved then it will just give you the average rate of change between those two points.

Rounded Decimals

If you get a decimal result then it may have been rounded. This means the result may be slightly different.

Units

If the coordinates are measurements then ensure you use the same units.

Graph

Just knowing the slope won’t give you the full equation or shape of the graph.

If you are doing an important calculation for your studies, engineering or construction then ensure your coordinates are correct and the result is what you want.

FAQ’s

What is a Slope Calculator?

A Slope Calculator is an online maths tool used to calculate the slope of a straight line using 2 coordinate points. This tells you how steep the line is and whether it goes up, down or flat.

Is it free to use?

Yes, many Slope Calculators online are free. Simply input 2 sets of coordinates and calculate the slope.

What is the formula for slope?

The standard formula for finding the slope is m = (y2 - y1)/(x2 - x1). This finds the difference between the y coordinates and divides it by the difference between the x coordinates.

Can it calculate negative slopes?

Yes. Depending on your coordinates you can calculate positive, negative, zero and undefined slopes. A negative slope means the line is going down from left to right.

Can I use it on my Smartphone?

Yes. Most Slope Calculators online can be used on Smartphones, Tablets, Laptops and Desktops. Simply open your modern browser.