Midpoint Calculator
Enter two points to find the midpoint of the segment between them, or switch modes to find the missing endpoint when you know the midpoint and one end.
Last updated November 3, 2026
Result
Midpoint = (5, 7)
| Midpoint x | 5 |
|---|---|
| Midpoint y | 7 |
| Segment length | 8.485281 |
| Half length | 4.242641 |
Show the work
Formula: midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
- Points: (2, 4) and (8, 10).
- x = (2 + 8) / 2 = 5.
- y = (4 + 10) / 2 = 7.
Result: Midpoint = (5, 7)
The midpoint formula
midpoint = ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2)
The midpoint of a line segment is the point exactly halfway between its two endpoints. To find it, average the x coordinates and average the y coordinates separately. The pair of averages is the midpoint, and it lies on the segment at equal distance from both ends.
The calculator also shows the length of the segment, which is √((x2 − x1)² + (y2 − y1)²), and half of that length, the distance from the midpoint to either end. The order of the two points does not change the answer, because adding is the same in either order.
The second mode works backwards. If you know one endpoint and the midpoint, the other endpoint is 2 × midpoint − known endpoint, taken for x and y separately. This is the same as reflecting the known endpoint through the midpoint.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Geometry Calculator, Distance Calculator and Perimeter Calculator.
Negative and decimal coordinates
The formula works the same with negative numbers and decimals. For (−3, 1.5) and (5, −4) the x average is (−3 + 5) ÷ 2 = 1 and the y average is (1.5 − 4) ÷ 2 = −1.25, so the midpoint is (1, −1.25).
When the two points are opposite each other through the origin, such as (−4, −2) and (4, 2), the midpoint is (0, 0). The calculator never shows a negative zero, so that answer appears as a plain 0.
Finding a missing endpoint
Suppose a segment has one end at (4, 5) and its midpoint at (1, −2). The other end is (2 × 1 − 4, 2 × (−2) − 5) = (−2, −9). Checking in reverse, the midpoint of (4, 5) and (−2, −9) is (1, −2), which matches.
This is handy for diameters of circles. If one end of a diameter is known and the center is known, the center plays the role of the midpoint and the formula gives the opposite end of the diameter.
Perpendicular bisectors and circle centers
The perpendicular bisector of a segment passes through its midpoint at a right angle. For the points (2, 4) and (8, 10) the segment has slope 1, so the bisector has slope −1 and passes through (5, 7). Its equation is y = −x + 12.
If the two points are the ends of a diameter, the midpoint is the center of the circle and half the segment length is the radius. For (2, 4) and (8, 10) the center is (5, 7) and the radius is about 4.242641. Use the Slope Calculator to get the slope of the segment first.
On a number line and in other dimensions
On a number line the midpoint of 3 and 11 is (3 + 11) ÷ 2 = 7, which is also the average of the two numbers. The same idea extends to three dimensions by averaging a third coordinate; this calculator handles two dimensions, the usual case for graphs and coordinate geometry.
A point a quarter of the way along a segment is not the midpoint. It is p1 + 0.25 × (p2 − p1), which for (2, 4) and (8, 10) is (3.5, 5.5). The midpoint is the special case where the fraction is one half.
How to use the Midpoint Calculator
- Choose Midpoint of two points, or Missing endpoint if you know a midpoint.
- Enter the x and y values of the first point.
- Enter the second point, or the midpoint in the missing endpoint mode.
- Read the result and the segment length, then use Copy, Print or Share.
Worked example
For the points (2, 4) and (8, 10), the x average is (2 + 8) ÷ 2 = 5 and the y average is (4 + 10) ÷ 2 = 7, so the midpoint is (5, 7). The segment length is √(6² + 6²) = √72 ≈ 8.485281 and half of it is about 4.242641.
| Point 1 | Point 2 | Midpoint |
|---|---|---|
| (0, 0) | (6, 8) | (3, 4) |
| (−4, −2) | (4, 2) | (0, 0) |
| (1, 9) | (7, 3) | (4, 6) |
| (2.5, −1) | (6.5, 3) | (4.5, 1) |
Frequently asked questions
What is the midpoint formula?
It is ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2). Add the two x values and halve them, then add the two y values and halve them.
Does the order of the points matter?
No. Swapping the two points gives the same midpoint and the same segment length, because addition does not depend on order.
How do I find an endpoint from the midpoint?
Choose the Missing endpoint mode, enter the known endpoint and the midpoint, and the calculator returns 2 × midpoint − known endpoint for x and y.
Can the two points be the same?
Yes. The midpoint is then that same point and the segment length is 0. This is allowed here, unlike the slope of a line, which needs two different points.
Are my numbers stored or sent anywhere?
No. The calculation runs in your browser and nothing you enter is saved or uploaded unless you copy or share a link yourself.