CalConverters

Midpoint Calculator

Find the exact midpoint between two coordinates (x1,y1) and (x2,y2), or solve for a missing endpoint given one endpoint and the midpoint.

Loading calculator…

The midpoint formula

The midpoint MM of the segment joining (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

M=(x1+x22,  y1+y22)M = \left(\frac{x_1 + x_2}{2}, \; \frac{y_1 + y_2}{2}\right)

Each coordinate of MM is just the average of the matching coordinates of the two endpoints — the point equally far from both, along the straight segment connecting them.

Tip: A midpoint coordinate doesn't have to be a whole number. Whenever the two matching coordinates add up to an odd number, the average is a half-integer like −0.5-0.5 — that's the exact answer, not a rounding error.

Worked example

For (3,3)(3, 3) and (−4,−7)(-4, -7):

M=(3+(−4)2,3+(−7)2)=(−12,−2)=(−0.5,−2)M = \left(\frac{3 + (-4)}{2}, \frac{3 + (-7)}{2}\right) = \left(-\frac{1}{2}, -2\right) = (-0.5, -2)

For whole-number coordinates like (6,3)(6, 3) and (12,7)(12, 7), the midpoint is a whole number too: M=(9,5)M = (9, 5).

Finding a missing endpoint

Sometimes the midpoint is already known, along with just one endpoint — for example, the midpoint of a circle's diameter is its center, and the center plus one point on the circle determines the point directly opposite it. Solving the midpoint formula for the unknown endpoint gives:

x2=2xM−x1,y2=2yM−y1x_2 = 2x_M - x_1, \qquad y_2 = 2y_M - y_1

Example: endpoint (6,−4)(6, -4), midpoint (1,7)(1, 7):

x2=2(1)−6=−4,y2=2(7)−(−4)=18x_2 = 2(1) - 6 = -4, \qquad y_2 = 2(7) - (-4) = 18

So the missing endpoint is (−4,18)(-4, 18).

Tip: The most common mistake here is subtracting instead of doubling first — it's 2xM−x12x_M - x_1, not xM−x1x_M - x_1. Doubling the midpoint before subtracting is what "undoes" the original averaging.

Distance between the endpoints

Because a segment's two endpoints and its midpoint all sit on the same straight line, this calculator also reports the exact distance between the two endpoints (see the Distance Between Two Points calculator for the full formula) — useful when you need both the midpoint and the segment's length in one step.

Where midpoints show up

  • Geometry: the center of a circle is the midpoint of any diameter.
  • Construction and design: finding the exact center of a wall, beam, or shape to balance or divide it evenly.
  • Graphics and animation: interpolating a point exactly halfway between two positions.

Frequently asked questions

What is the midpoint formula?
The midpoint MM of the segment joining (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) is M=(x1+x22,y1+y22)M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) — simply the average of the two x-coordinates and the average of the two y-coordinates.
Why is the midpoint just an average of the coordinates?
A point exactly halfway between two endpoints is, by definition, equally far from both. Averaging each coordinate spreads the total difference evenly in both directions, which is exactly what "equally far from both" means for a straight segment.
What does it mean when the midpoint has a coordinate like -1/2?
It happens whenever the sum of the two matching coordinates is odd — dividing an odd number by 2 never lands on a whole number. For example 3+(−4)=−13 + (-4) = -1, and −1/2=−0.5-1/2 = -0.5 is a perfectly valid (and exact) midpoint coordinate, not a rounding artifact.
How do I find a missing endpoint if I know the midpoint and one endpoint?
Invert the midpoint formula: x2=2xM−x1x_2 = 2x_M - x_1 and y2=2yM−y1y_2 = 2y_M - y_1. This works because the midpoint formula says xMx_M is the average of x1x_1 and x2x_2 — multiplying by 2 undoes the averaging, and subtracting x1x_1 isolates the unknown endpoint.
What is a common mistake when finding the missing endpoint?
Subtracting instead of doubling first — the correct formula is x2=2xM−x1x_2 = 2x_M - x_1, not xM−x1x_M - x_1. Forgetting the factor of 2 is the single most common error, since it looks superficially similar to the ordinary midpoint formula.
Does it matter which point I call (x1,y1) and which I call (x2,y2)?
No. Addition doesn't care about order, so swapping the two endpoints gives the exact same midpoint. This is different from the distance and slope calculators, where swapping the points flips signs along the way (though the final answer still comes out the same).
How is this related to the Distance and Slope calculators?
All three take the same two points (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) and extract a different fact about the segment between them: Distance finds its length, Slope finds its steepness, and Midpoint finds the point exactly halfway along it.

Related calculators