Midpoint Calculator

What this calculator does

So, you have two points on a coordinate grid and you want the point exactly halfway between them. This tool finds it. Enter the coordinates of the two points and it returns the midpoint, the point sitting dead centre on the line segment joining them.

Four inputs, the x and y of each point, and the midpoint comes back rounded to one decimal place.

How to use it

1. Enter the coordinates of the first point, its x and its y.
2. Enter the coordinates of the second point.
3. Press Calculate.

What the midpoint is

The midpoint of a line segment is the point that divides it into two equal halves. It is the same distance from each of the two ends, sitting right in the middle of the straight line between them. On a coordinate grid, every point is described by an x and a y, and the midpoint has its own pair of coordinates. Finding it is one of the first tasks in coordinate geometry, and it turns up any time you need the centre of something defined by two points.

Averaging the coordinates

The way to find the midpoint is beautifully simple: you average the two x values and average the two y values. The midpoint's x is the first x plus the second x, divided by two, and its y is the first y plus the second y, divided by two. That is all there is to it. This makes sense because the middle of two numbers is just their average, and a point is only two numbers, one for each direction. The tool does exactly this, taking the mean of the two x coordinates and the mean of the two y coordinates.

A worked example

Take the points 2 comma 4 and 6 comma 8. For the x coordinate of the midpoint, average 2 and 6 to get 4. For the y coordinate, average 4 and 8 to get 6. So the midpoint is 4 comma 6. You can sense-check it: 4 comma 6 sits squarely between the two points, the same step away from each.

Where the midpoint is useful

The midpoint shows up in plenty of practical settings. In geometry it locates the centre of a line segment, which is the first step in bisecting it or finding the centre of a circle drawn through two points. On a map or a plan, it gives the halfway meeting point between two places. In design and graphics it helps centre and align objects. Anywhere you have two positions and want the balance point between them, averaging their coordinates gives the answer.

Going the other way

Sometimes you have the puzzle in reverse: you know one end of a segment and its midpoint, and you want the other end. That is a different calculation, since you are undoing the averaging rather than doing it. The endpoint calculator handles that case, working backwards from a start point and a midpoint to find the far end. This tool and that one are two halves of the same idea, one finding the middle from the ends, the other finding an end from the middle.

Questions people ask

What is the midpoint of two points?

The point exactly halfway between them, the same distance from each and sitting in the centre of the segment joining them.

How is it calculated?

By averaging the coordinates: the midpoint's x is the mean of the two x values, and its y is the mean of the two y values.

Why does averaging work?

Because the middle of two numbers is their average, and a point is just two numbers, one in each direction.

Does the order of the points matter?

No. Averaging gives the same result whichever point you enter first.

What if I know the midpoint and one end?

Then use the endpoint calculator, which works backwards to find the other end.

References

On the midpoint. The midpoint of a segment divides it into two equal parts and is found by averaging the endpoint coordinates.

1. Eric W. Weisstein, "Midpoint," from MathWorld, a Wolfram resource, on the point dividing a segment into two equal lengths and its coordinate formula.
2. "Cartesian coordinates," Encyclopaedia Britannica, on describing points in the plane by pairs of numbers.