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Midpoint Calculator

Calculate the midpoint of the line segment joining two points.

How it is calculated

The midpoint of a segment is the average of the endpoints, computed separately for each axis: M = ((x1 + x2) / 2, (y1 + y2) / 2). The inputs are the coordinates of the two endpoints, (x1, y1) and (x2, y2), in any consistent unit; the answer is in the same unit. Negative coordinates are allowed and are handled by ordinary addition, so a negative value pulls the average down. All four fields must be filled in. The results mx and my are shown to two decimals. The order of the two points does not matter, because addition is commutative, and the midpoint is always on the straight segment between them.

Worked example

Take the points (2, -3) and (8, 5). For the x coordinate: (2 + 8) / 2 = 10 / 2 = 5, shown as 5.00. For the y coordinate: (-3 + 5) / 2 = 2 / 2 = 1, shown as 1.00. The midpoint is therefore (5.00, 1.00). A quick check: it lies 3 units right and 4 units up from the first point, and the same distance from the second.

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Common mistakes

  • Subtracting instead of adding coordinates, which gives half the difference rather than the centre.
  • Mishandling a minus sign: -3 + 5 is 2, not -8.
  • Averaging x with y values from the wrong points, such as (x1 + y2) / 2.
  • Using the midpoint formula for the average of more than two points, where a centroid with the number of points as divisor is needed.

Sources

About this calculator

This calculator finds the midpoint of the line segment joining two points on a coordinate plane by averaging their x-coordinates and averaging their y-coordinates separately — the point exactly halfway between them in both directions. It's one of the most fundamental operations in coordinate geometry, sitting alongside distance and slope as a building block for more advanced problems.

Students use it to solve geometry and algebra problems involving line segments, perpendicular bisectors and circle centers (a circle's center is the midpoint of any diameter). Outside the classroom, mapping and GIS applications use the same averaging idea — adapted for latitude and longitude — to find a point centered between two locations, and designers use it to center objects or align elements precisely on a canvas.

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Comments (1)

  • Editorial team

    The midpoint is a handy way to find the centre of a circle when you know the two ends of a diameter, and the radius is then half the distance between those ends. You can verify an answer by checking that both endpoints are the same distance from it. The tool works in two dimensions; for 3D points, average the z values yourself. Would a third coordinate be useful to you?

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