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Midpoint Formula Calculator | Find Midpoint Between Two Points

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Find the midpoint of a line segment from its two endpoints using the average formula — add the coordinates and divide by two — with the working shown for 2D and 3D points. The essential geometry tool for bisectors, circle centers and coordinate problems.

Last updated: June 2026 · Free · No sign-up required

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Results

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Quick reference

PointsMidpoint
(0,0) & (4,6)(2, 3)
(-2,3) & (4,-1)(1, 1)
(1,5) & (1,9)(1, 7)

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Interpretation guide

Related formulaExpression
Midpoint((x1+x2)/2, (y1+y2)/2)
Distance√((x2-x1)² + (y2-y1)²)
Slope(y2-y1)/(x2-x1)

lightbulb Worked example: placing a halfway marker

A surveyor needs a fence post exactly halfway between two boundary markers at (1, 2) and (9, 8) on the site grid, with coordinates in meters. Averaging each coordinate: Mx = (1 + 9) / 2 = 10 / 2 = 5, and My = (2 + 8) / 2 = 10 / 2 = 5.

Result: The midpoint is (5, 5).

What this means: The post goes at (5, 5) — 4 m in x and 3 m in y from each marker, so it sits exactly equidistant from both. Averaging coordinates always lands on the segment itself, which is why the same formula also locates circle centers from diameters and rectangle centers from opposite corners.

Formula & methodology

Formula: Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

How the midpoint is computed

The midpoint of a segment is the point halfway between its endpoints, found by averaging each coordinate separately:

Midpoint = ( (x₁ + x₂) / 2 , (y₁ + y₂) / 2 )

  • Add the two x-coordinates and divide by 2 for the midpoint's x-value.
  • Add the two y-coordinates and divide by 2 for the midpoint's y-value.
  • For 3D points, average the z-coordinates the same way: (z₁ + z₂) / 2.

Why averaging works

Moving from one endpoint to the midpoint covers exactly half the displacement in x and half in y, so the result is equidistant from both endpoints. That property makes the midpoint the standard tool for finding circle centers from diameters, segment bisectors, and rectangle centers from opposite corners.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is the midpoint formula?
The midpoint between two points (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2). You average the x-values and average the y-values. The result is the point exactly halfway along the line segment connecting the two endpoints.
How do you find the midpoint between two points?
Add the two x-coordinates and divide by 2, then add the two y-coordinates and divide by 2. For (0, 0) and (4, 6): x = (0 + 4)/2 = 2 and y = (0 + 6)/2 = 3, so the midpoint is (2, 3). The same averaging works in three dimensions by also averaging z.
Can the midpoint have negative or fractional coordinates?
Yes. Averaging can produce negatives or fractions depending on the endpoints. For (-2, 3) and (1, 4), the midpoint is (-0.5, 3.5). There is nothing special required — you simply average each coordinate, and the result is wherever the exact center falls.
What is the difference between midpoint and distance?
The midpoint is the center point of a segment, found by averaging coordinates. The distance is the length of the segment, found with the distance formula √((x2-x1)² + (y2-y1)²). One gives a location (a point); the other gives a length (a number).
How do I find an endpoint if I know the midpoint?
Use the midpoint equations in reverse. If M is the midpoint of A and B and you know A and M, then B = (2Mx - Ax, 2My - Ay). For example, with A = (1, 2) and midpoint (4, 5), the other endpoint is (2 x 4 - 1, 2 x 5 - 2) = (7, 8).
How do you find the midpoint in three dimensions?
Average the z-coordinates as well: the midpoint of (x1, y1, z1) and (x2, y2, z2) is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2). For (2, 4, 6) and (8, 10, 14): x = (2+8)/2 = 5, y = (4+10)/2 = 7, z = (6+14)/2 = 10, so the midpoint is (5, 7, 10). This calculator shows the working for both 2D and 3D points.
How can the midpoint find the center of a circle?
The center of a circle is the midpoint of any of its diameters. If a diameter runs from (1, 2) to (7, 8), the center is ((1+7)/2, (2+8)/2) = (4, 5). The same trick gives the center of a rectangle from opposite corners, which is why the midpoint formula shows up constantly in graphics, CAD, and game development.
Why does averaging the coordinates give the exact halfway point?
Because averaging each coordinate separately moves exactly half the total displacement in every direction. If M = ((x1+x2)/2, (y1+y2)/2), the distance from M to either endpoint equals precisely half the segment length — that is the definition of halfway. No square roots are involved, so the midpoint computes faster than the segment length does.
How many decimal places do the results show?
The midpoint is computed in full floating-point precision, so (0, 0) and (1, 3) give exactly (0.5, 1.5) rather than a rounded estimate. Each intermediate sum and division is displayed, so you can verify the arithmetic digit by digit. Halves always terminate cleanly — long decimals appear only when the coordinates themselves demand them.

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