3D Midpoint Calculator

COORDINATE AVERAGES / EQUAL HALF-SHIFTS

Find the center of a 3D segment one coordinate at a time

Use this explainer when you need to prove that a point is exactly halfway between two 3D coordinates, not just accept three averaged numbers. With the reviewed default points A = (2, 4, 6) and B = (8, 10, 12), the calculator averages each coordinate independently to return M = (5, 7, 9). The same output also shows that the first half-shift (3, 3, 3) matches the second half-shift (3, 3, 3).

Worked default example

Entered endpoints

First point A = (2, 4, 6). Second point B = (8, 10, 12).

Average the x-coordinates

x-mid = (x1 + x2) / 2 = (2 + 8) / 2 = 5.

Average the y-coordinates

y-mid = (y1 + y2) / 2 = (4 + 10) / 2 = 7.

Average the z-coordinates

z-mid = (z1 + z2) / 2 = (6 + 12) / 2 = 9.

Returned midpoint

Read the main result and the two supporting metrics together: M = (5, 7, 9).

Halfway check

A to M = (3, 3, 3) and M to B = (3, 3, 3), so the point returned by the calculator sits exactly halfway along the same straight segment.

What to enter and how to read the result

Enter x, y, and z for the first endpoint and x, y, and z for the second endpoint on one Cartesian coordinate system and one consistent unit scale. The main result card reports the midpoint x-coordinate first. The two supporting metrics underneath report midpoint y and midpoint z, and all three values together form the midpoint (5, 7, 9).

What the calculator actually does

Nirmion evaluates the coordinate-wise midpoint formula M = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2). In the reviewed default example, the calculator averages 2 and 8 to get 5, 4 and 10 to get 7, and 6 and 12 to get 9. Because each coordinate is averaged independently, the returned point creates two equal segment steps: (3, 3, 3) from A to M and (3, 3, 3) from M to B.

Where this model stops helping

Use this page only for straight segments in one Cartesian frame. It does not calculate a midpoint on a road network, a curved path, a weighted center of mass, or a midpoint between latitude and longitude on Earth's surface. Mixed units, mixed coordinate systems, and projected map data need conversion before you apply this formula.

Reference and next checks

The linked OpenStax section states the midpoint rule as coordinate-wise averaging in rectangular coordinates. This 3D calculator applies that same averaging step to z as well, which is the same workflow used by the reviewed calculator definition. If you need the straight-line distance of the same segment, the distance from a point to a plane, or the magnitude of a translated 3D vector, use the related calculators below.