Midpoint Calculator
Find the midpoint between two coordinate endpoints in 2D or 3D. You can also solve the reverse endpoint task when one endpoint and the midpoint are known.
How to Find the Midpoint
The midpoint of a line segment is the point halfway between endpoint A and endpoint B. In coordinate geometry, each midpoint coordinate is the average of the matching endpoint coordinates.
M is the midpoint, and x1, y1, x2, y2 are the endpoint coordinates in 2D.
M is the 3D midpoint; z1 and z2 add the third coordinate.
Supported Midpoint Tasks
| Mode | Inputs | Result |
|---|---|---|
| Midpoint | coordinates of A and B | point M in 2D or 3D |
| Missing endpoint | endpoint A and midpoint M | endpoint B |
| Check | points A, B, and M | segment length and equal halves |
- The main search intent is the coordinate midpoint between two endpoints.
- The reverse endpoint mode uses the same midpoint relationship in the opposite direction.
- The 2D mode includes a simple plot; 3D results stay numeric because a spatial plot is a different interaction.
How to Find a Missing Endpoint
If endpoint A and midpoint M are known, endpoint B is the point mirrored across M. For each coordinate, double the midpoint coordinate and subtract the matching coordinate of A.
B is the missing endpoint, M is the midpoint, and A is the known endpoint.
| Known | Find | Meaning |
|---|---|---|
| A and M in 2D | B with x and y | point reflection across M |
| A and M in 3D | B with x, y, and z | the same operation on every coordinate |
| A, B, and M | length check | M should split AB into two equal parts |
Input Limits and Rounding
- Enter coordinates as decimal numbers. Convert fractions or constants to decimal values first.
- The calculator returns rounded numeric results, not exact symbolic radicals.
- 3D mode computes coordinates and length, but does not render a 3D plot.
- A midpoint is the equal-part case of segment division; arbitrary ratios need a different calculator.
Worked Examples
Midpoints appear in triangle medians, diameters, symmetry problems, and coordinate proofs. They are also a common step before finding segment length or a line equation from two points.
| A | B | Midpoint M |
|---|---|---|
| (0, 0) | (4, 6) | (2, 3) |
| (-3, 5) | (7, -1) | (2, 2) |
| (1, 1, 1) | (5, 7, 9) | (3, 4, 5) |
| (-2, 0, 4) | (6, 8, 0) | (2, 4, 2) |
| (2.5; 1.5) | (−1.5; 4.5) | (0.5; 3) |
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Calculate the length of a line segment from endpoint coordinates in 2D or 3D, with midpoint, coordinate differences, direction vector, and a 2D preview.
Calculate the Euclidean distance between two points in 2D or 3D coordinates, with midpoint, coordinate differences, Manhattan distance, Chebyshev distance, and angle.
Find the equation of a line from two points or from a point and slope, with standard form, slope-intercept form, point-slope form, intercepts, and a graph.