How this works
The midpoint of a line segment is the point exactly halfway between its two endpoints. To find it, you average the x-coordinates and average the y-coordinates of the endpoints. Geometrically, the midpoint divides the segment into two equal halves, and it sits on the perpendicular bisector of the segment — the unique line passing through the midpoint at a right angle.
Midpoints come up in surprisingly many places. In coordinate geometry they're a building block for finding centroids of polygons, circumcenters of triangles, and the centers of circles defined by three points. In computer graphics and games, midpoints are used in subdivision algorithms (Bezier curves, mesh refinement). In statistics, the median can be defined as the midpoint of the middle two values when n is even. In real-world planning, "where should we meet halfway?" is literally a midpoint question.
This calculator generalises naturally to higher dimensions: in 3D, average all three coordinates; in n-D, average each. The same formula also works for weighted midpoints if you want the result to favour one endpoint — but this tool gives the standard equal-weight midpoint.
The formula
(x₁, y₁) and (x₂, y₂) are the endpoints. The standard midpoint corresponds to weight w = 0.5 in the weighted form. For 3D space, add a z-coordinate term; for higher dimensions, average each coordinate independently.
Example calculation
- Midpoint between (1, 2) and (4, 8).
- x_mid = (1 + 4) / 2 = 2.5; y_mid = (2 + 8) / 2 = 5. Midpoint = (2.5, 5).
- In 3D between (0, 0, 0) and (4, 6, 10): midpoint = (2, 3, 5).
Frequently asked questions
Is the midpoint always inside the segment?
Yes — the midpoint is by definition the point at parameter 0.5 along the segment from one endpoint to the other. It lies exactly on the segment and exactly halfway between the endpoints. Other "interior" points (e.g. the point one-third of the way along) exist but aren't called midpoints.
How do I find the midpoint of a triangle (centroid)?
Triangles don't have a single midpoint — but they have a centroid (center of mass), which is the average of all three vertices: ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3). Same idea as the segment midpoint but for three points instead of two. The centroid is also where the three medians (lines from each vertex to the midpoint of the opposite side) intersect.
Can I find a point that's 1/3 or 2/3 of the way?
Yes — use linear interpolation: point at parameter t = (x₁ + t·(x₂ − x₁), y₁ + t·(y₂ − y₁)) where t goes from 0 (point 1) to 1 (point 2). t = 0.5 gives the midpoint; t = 1/3 gives the point one-third of the way from point 1; t = 2/3 gives two-thirds. This is the foundation of every "blend between A and B" operation in graphics, animation, and signal processing.