# Midpoint Calculator

## Calculator Use

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Use this calculator to calculate the midpoint, the distance between 2 points, or find an endpoint given the midpoint and the other endpoint.

### Midpoint and Endpoint Calculator Solutions

Input two points using numbers, fractions, mixed numbers or decimals. The midpoint calculator shows the work to find:

- Midpoint between two given points
- Endpoint given one endpoint and midpoint
- Distance between two endpoints

The calculator also provides a link to the Slope Calculator that will solve and show the work to find the slope, line equations and the x and y intercepts for your given two points.

## How to Calculate the Midpoint

You can find the midpoint of a line segment given 2 endpoints, (x_{1}, y_{1}) and (x_{2}, y_{2}). Add each x-coordinate and divide by 2 to find x of the midpoint. Add each y-coordinate and divide by 2 to find y of the midpoint.

Calculate the midpoint, (x_{M}, y_{M}) using the midpoint formula:

It's important to note that a midpoint is the middle point on a line
*segment*. A true line in geometry is infinitely long in both directions. But a line segment has 2 endpoints so it is possible to calculate the midpoint. A ray has one endpoint and is infinitely long in the other direction.

### Example: Find the Midpoint

Say you know two points on a line segment and their coordinates are (6, 3) and (12, 7). Find the midpoint using the midpoint formula.

- First, add the x coordinates and divide by 2. This gives you the x-coordinate of the midpoint, x
_{M} - Second, add the y coordinates and divide by 2. This gives you the y-coordinate of the midpoint, y
_{M} - Take each result to get the midpoint. In this example the midpoint is (9, 5).

## How to Calculate Distance Between 2 Points

If you know the endpoints of a line segment you can use them to calculate the distance between the 2 points. Here you're actually finding the length of the line segment. Use the formula for distance between 2 points:

The formula for distance between points is derived from the Pythagorean theorem, solving for the length of the hypotenuse. See our Pythagorean Theorem Calculator for a closer look.

### Example: Find the Distance Between 2 Points

You know 2 points on a line segment and their coordinates are (13, 2) and (7, 10). Find the distance between the 2 points using the distance formula \( d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \)

- Insert your points (13, 2) and (7, 10) into the distance equation
- Complete the subtraction first since they're in parentheses
- Find the square of each term
- Add the results
- Find the square root and you've found the distance between the 2 points

Similar to this midpoint calculator is our Two Dimensional Distance Calculator. For distance between 2 points in 3 dimensions with (x, y, z) coordinates please see our 3 Dimension Distance Calculator.

## How to Calculate Endpoint

If you know an endpoint and a midpoint on a line segment you can calculate the missing endpoint. Start with the midpoint formula from above and work out the coordinates of the unknown endpoint.

- First, take the midpoint formula:
- And break it down so you have separate equations for the x and y coordinates of the midpoint
- Rearrange each equation so that you're solving for x
_{2}and y_{2}\( x_{2} = 2x_{M} - x_{1} \)\( y_{2} = 2y_{M} - y_{1} \) - Since you know the midpoint, insert its coordinates in place of
*x*and_{M}*y*in each equation_{M} - Insert the coordinates of your known endpoint into the values for
*x*and_{1}*y*_{1} - Finally, solve each equation to find
*x*and_{2}*y*which will be the coordinates of your missing endpoint_{2}

### Example: Find the Endpoint

Using the steps above, let's find the endpoint of a line segment where we know one endpoint is (6, -4) and the midpoint is (1, 7). The endpoint is the
*(x _{1}, y_{1})* coordinate. The midpoint is the

*(x*coordinate.

_{M}, y_{M})- First, take the midpoint formula:
- And rearrange the equations so that you're solving for x2 and y2
- Insert the coordinates of your midpoint (1, 7) in place of
*x*and_{M}*y*in each equation_{M} - Insert the coordinates of your known endpoint (6, -4) into the values for
*x*and_{1}*y*_{1} - Solve each equation to find
*x*and_{2}*y*._{2} - Your missing endpoint
*(x*is (-4, 18)_{2}, y_{2})