Case 1
- x₁ (first point)
- 0
- y₁ (first point)
- 0
- x₂ (second point)
- 4
- y₂ (second point)
- 6
(2, 3)
Open with these valuesMidpoint Calculator
(2, 3)
Result: (2, 3)The midpoint is the point exactly halfway along the segment between (x1, y1) and (x2, y2): midpoint = ((x1 + x2) / 2, (y1 + y2) / 2). For (0, 0) and (4, 6) that is (2, 3). Average the x-coordinates and the y-coordinates independently; the order of the two points never changes the answer.
Worked examples
Case 2
- x₁ (first point)
- -2
- y₁ (first point)
- -4
- x₂ (second point)
- 2
- y₂ (second point)
- 4
(0, 0)
Open with these valuesCase 3
- x₁ (first point)
- 1
- y₁ (first point)
- 2
- x₂ (second point)
- 4
- y₂ (second point)
- 8
(2.5, 5)
Open with these valuesHow it's calculated
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
- StepEnter the coordinates of the first point, x₁ and y₁.
- StepEnter the coordinates of the second point, x₂ and y₂.
- StepAdd the two x values and halve them; do the same for the two y values.
- ResultRead the centre point (mx, my) — it is equidistant from both endpoints.
What this number means
The midpoint of two points is the point that sits exactly halfway along the straight line connecting them — the centre of the segment. Given a first point (x1, y1) and a second point (x2, y2), it is found with the midpoint formula: midpoint = ((x1 + x2) / 2, (y1 + y2) / 2). Average the two x-coordinates to get the centre's x, and average the two y-coordinates to get its y. Each axis is handled on its own, and together they pin down the centre. Take (0, 0) and (4, 6): (0 + 4) / 2 = 2 is halfway across, (0 + 6) / 2 = 3 is halfway up, so the midpoint is (2, 3). That point is the same distance from each endpoint, and that distance is half the length of the whole segment. Because addition is commutative, the order of the points never changes the answer — swapping A and B gives the identical midpoint, and two identical points return that same point. Coordinates may be negative, zero or positive; the average handles the signs automatically, so (−2, −4) and (2, 4) meet at the origin. This one idea covers a lot of real work: the centre of a circle from a diameter, labels and anchors placed halfway in design, snapping objects to the middle in graphics and CAD, and a fair meeting point between two spots on a map.
The midpoint formula
Average the x-coordinates and the y-coordinates independently: midpoint = ((x1 + x2) / 2, (y1 + y2) / 2). Enter four numbers, read the centre point.
Order doesn't matter
Going from point A to B gives the same midpoint as B to A. Addition is commutative, so the centre never moves.
Flat plane, consistent units
This is the centre of the straight segment on a flat plane — not a point along a road, a curved path or a great circle, and it ignores any third dimension. The coordinates are unit-agnostic, so both points must use the same unit and the same scale.
Commonly misread
The midpoint is found by subtracting the coordinates.
Subtraction gives the distance between the points. The midpoint averages them: add and divide by 2 on each axis.
Starting from the other point gives a different midpoint.
It does not. Addition is commutative, so A to B and B to A give the identical centre.
Negative coordinates need a special case.
They do not. The average handles the signs on its own — (−2, −4) and (2, 4) meet at the origin (0, 0).
Reference table
| First point | Second point | Midpoint |
|---|---|---|
| (0, 0) | (4, 6) | (2, 3) |
| (1, 1) | (3, 3) | (2, 2) |
| (−2, −4) | (2, 4) | (0, 0) |
| (5, 0) | (5, 10) | (5, 5) |
| (1, 2) | (4, 8) | (2.5, 5) |
| (4, 6) | (0, 0) | (2, 3) |
| (2, 2) | (2, 2) | (2, 2) |
Questions
How do I find the midpoint between two points?
Use the midpoint formula: midpoint = ((x1 + x2) / 2, (y1 + y2) / 2). Add the two x-coordinates and divide by 2 to get the midpoint's x; do the same with the two y-coordinates to get its y. For (0, 0) and (4, 6) that is ((0 + 4) / 2, (0 + 6) / 2) = (2, 3).
What does the midpoint actually represent?
The midpoint is the point that sits exactly halfway along the straight line between the two points — the centre of the segment. It is the same distance from each endpoint, and that distance is half the length of the segment. Averaging each coordinate independently is the whole idea: the average x lands halfway across, the average y halfway up.
Does the order of the two points matter?
No. Addition is commutative, so (x1 + x2) / 2 equals (x2 + x1) / 2, and the same holds for the y-coordinates. You get the identical midpoint whether you start from point A or point B.
Can I use negative or zero coordinates?
Yes. Coordinates can be negative, zero or positive, and the average handles the signs automatically. For (−2, −4) and (2, 4) the midpoint is (0, 0) — the origin sits exactly halfway between two opposite points.
What is the difference between the midpoint and the distance?
They answer different questions about the same two points: the distance is how far apart they are, a single length found with √((x2 − x1)² + (y2 − y1)²). The midpoint is where the centre between them lies, a point found by averaging the coordinates. The midpoint is therefore always the same distance from each endpoint.
Where is the midpoint formula used?
Anywhere you need the centre between two positions: geometry homework, the centre of a circle from a diameter, labels and anchors placed halfway in design work, a fair meeting point between two spots on a map, and snapping objects to the middle in graphics and CAD tools.
Sources and last check
Information, not professional advice.