Midpoint Calculator
Midpoint of two points in 2D or 3D by ((x₁ + x₂)/2, (y₁ + y₂)/2), or a missing end point by B = 2M − A, with the working shown and exact sums. How it works
Use the Midpoint Calculator
About the Midpoint Calculator
The midpoint of (1, 2) and (7, 10) is (4, 6): average the x-values and average the y-values. This midpoint calculator takes two points in the plane, applies ((x₁ + x₂)/2, (y₁ + y₂)/2) and shows the formula with your numbers, in exact decimals. It also works in 3D and finds a missing end point from the midpoint, B = 2M − A.
Worked midpoints
| Point A | Point B | Midpoint |
|---|---|---|
| (0, 0) | (10, 10) | (5, 5) |
| (1, 2) | (3, 4) | (2, 3) |
| (1, 2) | (7, 10) | (4, 6) |
| (-4, 7) | (6, -1) | (1, 3) |
| (3, 8) | (-1, 4) | (1, 6) |
| (-3, -5) | (-9, -2) | (-6, -3.5) |
| (2.5, -3) | (7, 4.5) | (4.75, 0.75) |
| (0.1, 0.2) | (0.2, 0.4) | (0.15, 0.3) |
Frequently asked questions
- What is the midpoint formula?
- M = ((x₁ + x₂)/2, (y₁ + y₂)/2). For (-4, 7) and (6, -1): ((-4 + 6)/2, (7 + (-1))/2) = (2/2, 6/2) = (1, 3).
- How do you find the other endpoint from the midpoint?
- Double the midpoint and subtract the known endpoint: B = 2M − A. With A = (3, 8) and M = (1, 6), B = (2 − 3, 12 − 8) = (-1, 4). With decimals it works the same way: A = (2.5, -1) and M = (0.5, 1.5) give B = (1 − 2.5, 3 − (-1)) = (-1.5, 4). Pick Find an end point and type A and M, and the tool writes B = 2M − A = (2 × 1 − 3, 2 × 6 − 8) = (-1, 4). Back in Find the midpoint, entering A = (3, 8) and B = (-1, 4) shows the midpoint (1, 6), which checks the answer.
- Can the coordinates be negative or decimals?
- Yes. (-3, -5) and (-9, -2) give (-6, -3.5), and (2.5, -3) and (7, 4.5) give (4.75, 0.75). The sums are exact, so 0.1 and 0.2 give 0.15.
- Is the midpoint the same as the average of the points?
- Yes. The midpoint’s x is the mean of the two x-values and its y is the mean of the two y-values, which is also the point halfway along the segment from A to B.
- Does it work for 3D points?
- Yes. Pick 3D (x, y, z) and the third coordinate is averaged the same way, (z₁ + z₂)/2: (1, 2, 3) and (5, 8, -1) give (3, 5, 1). Find an end point works in 3D too.
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