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Midpoint Calculator

Use this free midpoint calculator to find the point exactly halfway between two points. Enter the coordinates of both points — in 2D, or turn on the 3D toggle — and the calculator shows the midpoint and the distance between the points, with the working shown.

How it works

The midpoint is the point that sits exactly halfway between two points. If you draw a straight line segment between point A and point B, the midpoint is the point on that segment that is the same distance from A as it is from B. Finding it is simpler than it looks: you average the coordinates. The midpoint's x-coordinate is the average of the two x-coordinates, and its y-coordinate is the average of the two y-coordinates.

That is the whole formula. Add the two x-values together and divide by two; add the two y-values together and divide by two. The result is a point, written as an ordered pair, that lies dead center between the two points you started with. Because it is just an average, the midpoint always falls between the two points on each axis — its x is somewhere between x1 and x2, and its y is somewhere between y1 and y2.

In three dimensions the idea is exactly the same, with one more coordinate to average. The midpoint of (x1, y1, z1) and (x2, y2, z2) is ((x1 + x2) ÷ 2, (y1 + y2) ÷ 2, (z1 + z2) ÷ 2). Turn on the 3D toggle in this calculator and enter the z-values for both points to get the 3D midpoint and the 3D distance. The z-coordinate behaves like x and y — it is averaged on its own, and it never affects the other two coordinates.

This calculator also gives the distance between the two points, because the two questions usually come together. The distance formula is the Pythagorean theorem in disguise: the horizontal gap between the points and the vertical gap form the two short sides of a right triangle, and the straight-line distance is the hypotenuse. In 2D the distance is the square root of (x2 − x1)² + (y2 − y1)², and in 3D you add (z2 − z1)² under the square root as well.

Midpoints show up everywhere once you start looking for them. In geometry class they are used to bisect line segments and to find the center of a shape. In mapping and navigation, the midpoint of two locations is the natural meeting point — the fairest place for two people to meet. In construction and design, the midpoint marks where a support, a joint, or a center line belongs. In computer graphics, midpoints are used to split curves and to place objects evenly. Any time something needs to be centered between two known points, the midpoint formula is the tool for the job.

A few details worth knowing: the midpoint of two identical points is the point itself. If the two coordinates add up to an odd number, the midpoint has a .5 in it — the midpoint of 1 and 2 is 1.5, which is exactly halfway, not rounded. Negative coordinates work the same way as positive ones, so the midpoint of −4 and 6 is 1. And the midpoint formula works no matter how far apart the points are or which quadrant they sit in; the average always lands in the middle.

Worked example

Find the midpoint and the distance between A (2, 3) and B (6, 11).

Step 1: Average the x-coordinates — (2 + 6) ÷ 2 = 8 ÷ 2 = 4.
Step 2: Average the y-coordinates — (3 + 11) ÷ 2 = 14 ÷ 2 = 7.
Step 3: The midpoint is (4, 7).
Step 4: Find the distance — the horizontal gap is 6 − 2 = 4 and the vertical gap is 11 − 3 = 8, so distance = √(4² + 8²) = √(16 + 64) = √80 ≈ 8.94.

So the midpoint of (2, 3) and (6, 11) is (4, 7), and the two points are 8.94 units apart. You can check the answer on the grid: (4, 7) sits exactly halfway along the segment from A to B, four units right and four units up from A, and four units left and four units down from B.

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