Midpoint Calculator — midpoint between two points

How it works

The midpoint of a line segment is the point dead-centre between its two endpoints. Finding it is just averaging: take the mean of the x-coordinates and the mean of the y-coordinates separately:

midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)

Averaging each coordinate lands you exactly halfway along in that direction, so the result is equidistant from both endpoints and sits right on the segment connecting them. It works for any points, including negatives, and gives half-integer values when the endpoints are an odd distance apart.

Worked example

Find the midpoint of (2, 4) and (6, 8). Average the x's and the y's:

• x: (2 + 6) ÷ 2 = 8 ÷ 2 = 4
• y: (4 + 8) ÷ 2 = 12 ÷ 2 = 6

So the midpoint is (4, 6). It works with negatives too: (−2, 3) and (4, −1) give ((−2 + 4) ÷ 2, (3 + −1) ÷ 2) = (1, 1). And endpoints an odd apart give a ".5" coordinate — (0, 0) to (3, 5) has midpoint (1.5, 2.5).

Frequently asked questions

How do I find the midpoint of two points?

Average each coordinate: add the two x-values and divide by 2 for the midpoint's x, then do the same for the y-values. For (1, 2) and (7, 6): ((1+7)/2, (2+6)/2) = (4, 4). That's all there is to it — one average per axis.

Why does averaging the coordinates give the midpoint?

Because the midpoint is halfway along in every direction, and the halfway value between two numbers is their average. Doing it independently for x and for y lands you at the centre of the segment, since the segment moves linearly in both coordinates at once.

Can the midpoint have decimal or negative coordinates?

Yes. If the endpoints differ by an odd number, the average is a half-integer — (0,0) and (1,1) have midpoint (0.5, 0.5). And if the points are in negative regions of the plane, the midpoint can be negative too. The formula handles all of these.

How is the midpoint related to distance?

The midpoint is the same distance from each endpoint — exactly half the total distance between them. So it splits the segment into two equal halves. If you need that half-length, use the distance calculator and halve the result, or measure from either endpoint to the midpoint.

What is the midpoint used for?

To find centres and averages of position: the centre of a line segment, the centre of a rectangle or circle from opposite corners/ends of a diameter, the balance point between two locations, or the centre of a bounding box. It's also the first step in constructing a perpendicular bisector.

Can I find the midpoint in three dimensions?

Yes — average the z-coordinates as well: ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). The idea is identical, one average per axis. This calculator covers the 2D (plane) case; add the z-average by hand for 3D points.