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Midpoint Calculator: Midpoint and Missing Endpoint
Find the exact middle of a line segment from its two endpoints, or work backwards to find the second endpoint when you know one endpoint and the midpoint. Includes segment length and slope.
The midpoint formula
The midpoint of a segment is the average of its endpoints, taken one coordinate at a time. For endpoints A(x1, y1) and B(x2, y2):
M = ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2)
This works because moving from A to B is a change of (x2 − x1, y2 − y1), and the middle is reached after half of that change. Adding half the difference to x1 gives x1 + (x2 − x1) ÷ 2, which simplifies to the average. The same rule extends to three dimensions by averaging the z coordinates as well.
Finding a missing endpoint
If you know one endpoint A and the midpoint M, the other endpoint B lies on the opposite side of M at the same distance. Rearranging the midpoint formula gives B = (2 × Mx − Ax, 2 × My − Ay). In other words, B is the reflection of A through M. Choose the missing-endpoint mode, enter A in the first pair of boxes and M in the second pair. For example, with A = (1, 2) and M = (4, 6), the other end is (7, 10), since 2 × 4 − 1 = 7 and 2 × 6 − 2 = 10.
Where midpoints are used
- Perpendicular bisectors: the perpendicular bisector of a segment passes through its midpoint at right angles. Combine the midpoint with the negative reciprocal slope from the slope calculator to write its equation.
- Circles: the centre of a circle is the midpoint of any diameter, so two opposite points on the circle give the centre directly.
- Parallelograms: the diagonals of a parallelogram share a midpoint, which is a quick way to find a missing vertex.
- Layout and design: centring an object between two marks is a midpoint calculation.
Common mistakes
The most frequent error is averaging x with y instead of x with x. Pair the coordinates by axis. A second slip is forgetting the factor of 2 when working backwards: the midpoint is not the difference between the points, and the missing endpoint is not simply M minus A. Negative values also deserve care, because (−3 + 5) ÷ 2 is 1, while many people subtract by habit. Finally, the midpoint of a segment is not the centroid of a shape with more points; for several points you average all of them, dividing by the count rather than by 2.
Worked example
A segment runs from (−3, 4) to (5, −10). Where is its midpoint?
Inputs
| What do you want to find? | Midpoint of two endpoints |
|---|---|
| Endpoint A: x1 | -3 |
| Endpoint A: y1 | 4 |
| Second point: x2 | 5 |
| Second point: y2 | -10 |
Result
The point exactly halfway between A and B.
| Working | M = ((-3 + 5) ÷ 2, (4 + -10) ÷ 2) |
|---|---|
| Segment length | 16.1245 |
| Half-length (each side of the midpoint) | 8.0623 |
| Slope of the segment | -1.75 |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do you find the midpoint of two points?
Add the two x coordinates and divide by 2, then add the two y coordinates and divide by 2. The pair of averages is the midpoint of the segment.
How do I find the other endpoint if I know the midpoint?
Double each midpoint coordinate and subtract the matching coordinate of the known endpoint. This places the second endpoint the same distance beyond the midpoint.
Is the midpoint always on the line between the points?
Yes. The midpoint lies on the segment itself, exactly halfway along it, so it is equally far from both endpoints.
Does the midpoint formula work in three dimensions?
Yes. Average the z coordinates in the same way as x and y. The calculator here handles two dimensions, and the logic extends directly.
What if the midpoint has decimals?
That is normal when the sums of the coordinates are odd. A midpoint of (2.5, 4) simply means the middle falls between whole grid positions.
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References and sources
- Standard coordinate geometry: the midpoint formula and its use in bisectors and parallelogram properties.