# Midpoint Calculator

Created by Mateusz Mucha and Piotr Małek
Reviewed by Jack Bowater
Last updated: Jul 02, 2023

The midpoint calculator will take two coordinates in the Cartesian coordinate system, and find the point directly in between both of them. This point is often useful in geometry. As a supplement to this calculator, we have written an article below that discusses how to find the midpoint and what the midpoint formula is.

If you want to understand how one coordinate changes with respect to another, we recommend checking the average rate of change calculator.

## How to find a midpoint

To determine the midpoint:

1. Label the coordinates (x₁,y₁) and (x₂,y₂).
2. Add both x and y values separately.
3. Divide each result by 2.
4. The new values form the coordinates of the midpoint.
5. Check your results using the midpoint calculator.

Suppose we have a line segment and want to cut that section into two equal parts. To do so, we need to know the center. We can achieve this by finding the midpoint. You could measure with a ruler or just use a formula involving the coordinates of each endpoint of the segment. The midpoint is simply the average of each coordinate of the section, forming a new coordinate point. We shall illustrate this below.

## Midpoint formula

If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x₃,y₃). The midpoint calculator will solve this instantaneously if you input the coordinates. Follow the steps above if calculating by hand.

For small numbers, it's easy to calculate the midpoint by hand, but with larger and decimal values, the calculator is the simplest and most convenient way to calculate the midpoint.

It is possible to divide a line segment into any given ratio, not just 1:1. Use our ratios of directed line segments calculator to learn how.

Just as finding the midpoint is often required in geometry, so is finding the distance between two points. The distance between two points on a horizontal or vertical line is easy to calculate, but the process becomes more difficult if the points are not aligned as such. This is often the case when dealing with the sides of a triangle. Therefore, the distance calculator is a convenient tool to accomplish this.

In some geometrical cases, we wish to inscribe a triangle inside another triangle, where the vertices of the inscribed triangle lie on the midpoint of the original triangle. The midpoint calculator is extremely useful in such cases.

## FAQ

### How do you find class midpoint?

1. Find the lower class limit. For a range of 2-5, this is 2.
2. Find the upper class limit. For the same range, it is 5.
3. Add the two numbers together. For us, this yields 7.
4. Divide the result by 2. The class midpoint of 2-5 is 3.5.

### How do you find the endpoint with the midpoint and the other endpoint?

2. Subtract your known endpoint to get the other. It doesn’t matter if it's the upper or lower bound.
3. Marvel at your mathematical skills!

### How do I find the midpoint of a triangle?

To find the midpoint of a triangle, known technically as its centroid, follow these steps:

1. Find the midpoint of the sides of the triangle. If you know how to do this, skip to step 4.

2. Measure the distance between the two endpoints, and divide the result by 2. This distance from either end is the midpoint of that line.

3. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates. The results give you the coordinates of the midpoint.

4. Draw a line between a midpoint and its opposite corner.

5. Repeat for at least one other midpoint and corner pair, or both, for the highest degree of accuracy.

6. Where all the lines meet is the centroid of the triangle.

### What is the midpoint of a circle?

To find the midpoint, or center, of a circle, follow these instructions:

1. Find two points on the circle that are completely opposite from each other, i.e., that is, they are separated by the diameter of the circle.

2. If you know their coordinates, add the two x coordinates together, and divide the result by 2. This is the x coordinate of the center.

3. Do the same for the 2 y coordinates, which will give you the y coordinate.

4. Combine the two to get the centroid’s coordinates.

5. If you do not know the coordinates, measure the distance between the two points and half it.

6. This half distance between one endpoint and the other is the midpoint.

### How do I find the midpoint of a square?

To find the midpoint, or centroid, of a square, follow this simple guide:

1. If you have the coordinates of two opposite corners of a square, add the 2 x coordinates together and divide the result by 2.

2. Do the same for the y coordinates.

3. Use these two calculated numbers to find the center of the square, as they are its x and y coordinates, respectively.

4. Alternatively, draw a line from one corner to the opposite corner, and another for the remaining pair.

5. Where these two lines cross is the square’s centroid.

### Do you round midpoints?

In general, you don’t round midpoints. You definitely do not for continuous data, as that point is a real point in a data set. For discrete data, you generally do not, instead noting that the midpoint is the value of both of the values either side of the midpoint calculation.

### What is the midpoint of 0 and 5?

2.5. To find the midpoint of any range, add the two numbers together and divide by 2. In this instance, 0 + 5 = 5, 5 / 2 = 2.5.

### How do you find the midpoint of a trapezoid?

You can find the midpoint, or centroid, of a trapezoid, by one of two methods:

1. Draw a line from one corner of the trapezoid to its opposing corner.
2. Do the same for the remaining pair of corners.
3. Where these two lines cross is the centroid.
4. Balance your trapezoid perfectly on its centroid!

Alternatively:

1. Take the coordinates of two opposite sides.
2. Add the x coordinates of these points together and divide by 2. This is the midpoint’s x coordinate.
3. Repeat for the 2 y coordinates, giving the midpoint’s y coordinate.

### What is the midpoint of 0,2 and 2,8?

1. Add 0 and 2 together to get 2.
2. Divide the result by 2, which results in 1. This is the x coordinate of the midpoint.
3. Add 2 and 8 together, which is 10.
4. Divide 10 by 2, the result of which is 5; this is the y coordinate of the midpoint.
5. Put the two coordinates together; the midpoint of (0,2) and (2,8) is (1,5).

### What is the midpoint of 30 and 60?

45. To find the midpoint of any two numbers, find the average of those two numbers by adding them together and dividing by 2. In this case, 30 + 60 = 90. 90 / 2 = 45.

Mateusz Mucha and Piotr Małek
First point coordinates
x₁
y₁
Second point coordinates
x₂
y₂ Midpoint
x midpoint
y midpoint
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