Midpoint Calculator

Midpoint Finder

Enter both points of the line segment to find the midpoint using this midpoint calculator. On hitting the calculate button, the answer appears at the bottom of the calculator with a step-by-step computation process for understanding.

How to use this midpoint calculator?

Follow the instructions below to operate this mid point finder.

1. Enter the x-coordinates of both points.
2. Similarly, enter the y-coordinates.
3. Hit the calculate button.

What is a midpoint?

The name gives away the meaning on its own. But for a formal definition, midpoint can be defined as:

    “Such a point in the cartesian plane which divides a line segment into two equal parts"

This new point is equally distanced from both starting and ending points. It is the bisector point of the line segment as every other line that divides the line segment in half passes through the midpoint.

Midpoint Formula:

The general formula to find the midpoint if the points A and B in a two-dimensional cartesian plane are (x₁,y₁) and (x₂,y₂) respectively;

The point made from these X and Y values is called the midpoint. To prove that this is the correct and logical formula, take this example.

The x₁ is 1 and x₂ is 3. By using the midpoint formula for x-coordinate, we get x_m equal to 2 which makes sense as the middle number between 1 and 3 is 2. 

The above formula is for a 2-d plane. But for 3 or more dimensions, the midpoint point is the average of x and y coordinates. 

Also, try the distance between two point calculator.

How to find the midpoint of a line segment?

You can calculate it using a ruler or compass as well. But as the values get higher, it becomes difficult to find a big enough ruler. 

The next choice is to use the midpoint formula. But this also has limitations because when values are much bigger and more complex, the chances of making a mistake are more. Thence, the last option is to use the midpoint formula calculator.  

To learn to find it yourself, read the solved example below.

Example:

Two points in a 2-dimensional plane are (9,0) and (4,5). Calculate the midpoint between these points. 

Solution:
Step 1: Identify the starting and ending points.

A = (x₁, y₁) = (9,0)
B = (x₂, y₂) = (4,5)

Step 2: Find the x-coordinate of the midpoint.

Step 3: Find the y-coordinate of the midpoint.

The midpoint is (13/2, 5/2).