Midpoint Calculator
Point A
Point B
Midpoint(5.0000, 5.0000)
X Coordinate5.0000
Y Coordinate5.0000
The midpoint of a line segment is the point exactly halfway between its two endpoints, found by averaging the x-coordinates and the y-coordinates. This calculator works both ways: give it two endpoints to get the midpoint, or give it one endpoint and the midpoint to recover the missing endpoint. Both modes are pure coordinate geometry with no rounding beyond display.
Formula
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
- x₁, y₁
- Coordinates of the first endpoint
- x₂, y₂
- Coordinates of the second endpoint
- M
- The midpoint of the segment
How it works
- In Find Midpoint mode, enter the coordinates of points A (x₁, y₁) and B (x₂, y₂); the calculator averages each pair of coordinates.
- The midpoint is ((x₁ + x₂) / 2, (y₁ + y₂) / 2) — the arithmetic mean of the two x-values and of the two y-values.
- In Find Endpoint mode, enter one endpoint and the known midpoint; the calculator reflects the endpoint through the midpoint using B = (2·mₓ − x₁, 2·m_y − y₁).
Worked example
Find the midpoint of the segment joining A(2, 3) and B(8, 7).
- Average the x-coordinates: (2 + 8) / 2 = 5.
- Average the y-coordinates: (3 + 7) / 2 = 5.
- Combine the averages into a single point.
The midpoint is (5, 5).
Frequently asked questions
- How do I find a midpoint between two points?
- Add the two x-coordinates and divide by two, then add the two y-coordinates and divide by two. The pair of averages is the midpoint, which lies exactly halfway along the segment.
- Can I find a missing endpoint if I know the midpoint?
- Yes. Switch to Find Endpoint mode, enter the endpoint you have and the midpoint, and the calculator returns the other endpoint using B = (2·mₓ − x₁, 2·m_y − y₁).
- Does the midpoint depend on which point is A and which is B?
- No. Because the formula averages the coordinates, swapping the order of the two endpoints gives exactly the same midpoint.
- How is this different from a distance calculator?
- A distance calculator measures how far apart two points are, while the midpoint calculator finds the point centered between them. This tool also reverses the process to locate a missing endpoint, which a distance calculator does not do.