Midpoint Calculator (2D + 3D)

Midpoint = (avg of each coordinate). The point exactly between two points in 2D or 3D.

Inputs

Result

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter two points.
  • Read midpoint coordinates.

About this calculator

The midpoint of two points is the average of their coordinates: M = ((x₁+x₂)/2, (y₁+y₂)/2). It's exactly halfway between, equidistant from both points. Used in geometry (constructing perpendicular bisectors), graphics (interpolation, mesh subdivision), and statistics (sometimes as median proxy).

Frequently asked

Why average?+
Average of two numbers is exactly halfway between them. Apply to each axis independently.
Generalize to 3D?+
Yes — m = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). And to any dimension.
How is this used?+
Constructing perpendicular bisector (line through midpoint, perpendicular to original). Bezier curve subdivision. Triangle medians.
What if points coincide?+
Midpoint is the same as both points. Distance is 0.
Centroid vs. midpoint?+
Midpoint: 2 points. Centroid: 3+ points (their average — the geometric center).

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