What this calculator does
The midpoint of two points is the single point exactly halfway between them, found by averaging their x-coordinates and averaging their y-coordinates separately. It always lies on the straight line joining the two points, precisely at its centre.
This calculator applies the midpoint formula directly: enter the coordinates of two points and it returns the coordinates of the point exactly between them, along with the distance from each original point to that midpoint.
The formula
The midpoint formula averages each coordinate independently: the x-coordinate of the midpoint is (x₁+x₂)/2, and the y-coordinate is (y₁+y₂)/2. Because it treats each axis separately, it works the same way regardless of how the two points are oriented relative to each other.
| Term | Meaning |
|---|---|
| (x₁, y₁) | The coordinates of the first point. |
| (x₂, y₂) | The coordinates of the second point. |
| Midpoint | The point ((x₁+x₂)/2, (y₁+y₂)/2), exactly halfway between the two. |
The inputs explained
| Field | What to enter |
|---|---|
| x₁ | The x-coordinate of the first point. |
| y₁ | The y-coordinate of the first point. |
| x₂ | The x-coordinate of the second point. |
| y₂ | The y-coordinate of the second point. |
When to use it
Finding the centre of a line segment
Any time a diagram, map reference or geometry problem needs the exact centre point of a segment defined by two endpoints, the midpoint formula gives it directly.
Locating the centre of a circle from its diameter
If two points on a circle are the ends of a diameter, their midpoint is the centre of the circle, which is often the first step before finding the radius or the circle’s equation.
Checking a geometry or coordinate-geometry answer
Midpoint questions appear throughout school-level coordinate geometry; running the same two points through here checks a hand-worked answer quickly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the midpoint moves as one point changes, along a fixed segment
The first point held at the origin, with the second point moving further out.
| x₂ | Midpoint |
|---|---|
| 2 | (1.000, 5.000) |
| 4 | (2.000, 5.000) |
| 6 | (3.000, 5.000) |
| 8 | (4.000, 5.000) |
| 10 | (5.000, 5.000) |
| 20 | (10.000, 5.000) |
Questions
What is the midpoint formula?
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). It averages the x-coordinates of the two points to get the midpoint’s x-coordinate, and does the same separately for the y-coordinates.
Is the midpoint always exactly between the two points?
Yes. The midpoint formula guarantees the result lies exactly halfway along the straight line segment connecting the two points, at an equal distance from each.
Can the midpoint formula be used in three dimensions?
The same averaging idea extends directly: add a z-coordinate and average that too, giving ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2) for two points in 3D space.
How is the midpoint different from the centroid of a triangle?
A midpoint applies to two points, and a centroid applies to three. The centroid of a triangle is the average of all three vertices’ coordinates, not the midpoint of any single side, though it does sit on the line from each vertex to the midpoint of the opposite side.
For the distance, slope and line equation between the same two points, see the fuller distance, midpoint and slope calculator. For the hypotenuse of a right triangle, see the hypotenuse calculator.