First line equation y = mx + r
Second line passes through point
Perpendicular line equation y = ax + b

Perpendicular Line Calculator

Finding the equation of lines is one of the most common calculations in vector Mathematics. Being a student, you must have been asked to find the equation of a perpendicular line using another line’s equation or coordinates. If you don’t know how to do this with accuracy, you should use this Perpendicular Line Calculator.

It is a free online maths calculator that can quickly find such an equation. This online calculator has been programmed for this purpose that adopts your given input values and uses them to find a line that will be perpendicular to the line you have inserted. If you want to know more about this tool and this specific type of line, read on till the end.

Perpendicular Line Definition

A perpendicular line is a specific term used for those lines that intersect another line or set of lines at an angle of 90 degrees. In simple words, a line that will cut another line vertically straight will be called a perpendicular line.

It is not compulsory that a line has only one line of this type. We can draw as many perpendicular lines as we need on a single line because we can draw a line making 90 degrees of angle on different points of the same line. In Mathematics, a perpendicular line is shown by inserting “” this symbol between the lines. For example, if the AB line is perpendicular to the CD line, it will be written as “AB ⫡ CD”.

Formula for a Perpendicular Line

There is no quick formula that we can write here in a single line. We have to derive its formula step by step to understand how you can calculate the perpendicular line.

Let us have a line with the following equation,

y = ax + b	

Now, we have to find the perpendicular line. Let’s assume the line has coordinates x0 and y0. So, we can write the equation of the new line (Perpendicular line) as,

y0 = mx0 + r 	

As we know that the product of the slopes of two perpendicular lines is equal to -1. So,

a * m = -1 r 	

It can also be written as,

a = -1/m 	

So, the equation of the perpendicular line will become,

y0 = -1/m * x0 + b 	
y0 = -x0/m + b	 

We can also rewrite the equation to find the value of b and complete the equation of a perpendicular line.

How to find the Perpendicular Line?

No doubt, it is a difficult task to find the equation of a perpendicular line. But we have solved an example here to let you understand it properly.

Example 1:

Find the equation of a line that passes through (4, 8) and is perpendicular to y = 4x + 6.


By comparing the given equations with the above formulas, we know,

m = 4 and r = 6	

Now, we have to find the values for “a” and “b” using the above equations/formulas.

a = -1/m 	 
a = -¼ 	   
a = -0.25 	  

The equation of the new line can be written as,

 y = -0.25x + b	    

Using the values of a point from which this line must pass,

8 = -0.25 (4) + b	    
8 = -1 + b	   
b = 9 	 

So, the final equation of the perpendicular line will be written as,

y = -0.25x +9	  

How to use a perpendicular line calculator?


It may be hard for you to find the equation or follow the above steps. You can use this online tool Calculator’s Bag by following these simple steps.

  • Insert the values related to the given line i.e. slope and value of “r”.
  • Write the coordinates of the point from which the line must pass
  • This calculator will show the line that will be perpendicular to the given line and pass through the point.

FAQ | Perpendicular Line Calculator

Are perpendicular lines always 90?

Yes, perpendicular lines must make an angle of 90 degrees to the line on which these are drawn.

Do perpendicular lines add up to 180?

A perpendicular line makes an angle of 90 degrees with another line. It is not a closed shape that will add up its angles to make 180 degrees.

What are perpendicular lines?

All lines that are drawn on other lines by making an angle of 90 degrees are called perpendicular lines.

Why is the product of slopes of two perpendicular lines equal to -1?

It is a rule of vector Mathematics that the slope of two perpendicular lines is equal to -1 because these are fully opposite to each other. .

Can perpendicular lines be noncoplanar?

Yes, Perpendicular lines can be noncoplanar.