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Midpoint Calculator

Enter two points to get the exact point halfway between them, in 2D or 3D. Already know the midpoint? Switch modes to find the missing endpoint. Steps, the segment length, a graph and evenly spaced points along the segment are included.

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How to use the Midpoint Calculator

  1. Choose the mode: midpoint, or endpoint from a midpoint.
  2. Pick 2D or 3D.
  3. Enter the coordinates of point A and of point B (or of the midpoint M).
  4. Read the result: the midpoint or the missing endpoint appears instantly.
  5. Review the steps, graph and table, or copy the results.

Midpoint formulas

TaskFormulaExample
Midpoint in 2DM = ((x₁ + x₂)/2, (y₁ + y₂)/2)(2, 3) and (8, −5) → (5, −1)
Midpoint in 3DM = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)(1, 2, 3) and (7, 8, 9) → (4, 5, 6)
Missing endpointB = (2xₘ − x₁, 2yₘ − y₁)A(−1, 4), M(3, 1) → B(7, −2)
Point at fraction tP = A + t(B − A)t = 0.25 of (0,0)→(8,4) → (2, 1)
Segment length√((x₂ − x₁)² + (y₂ − y₁)²)(2, 3) to (8, −5) → 10

Where midpoints are used

Midpoints show up throughout geometry and everyday work: finding the center of a circle from the ends of a diameter, bisecting a segment in a construction, locating the center of a board or wall for mounting, finding the halfway point between two map coordinates on a small flat area, and computing centroids. For points on the Earth over long distances, use a great-circle midpoint instead, because latitude and longitude are not a flat grid.

Frequently asked questions

What is the midpoint formula?

The midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2): average the x-coordinates and average the y-coordinates. In 3D, average the z-coordinates as well.

How do I find an endpoint from the midpoint?

Rearrange the formula: x₂ = 2·xₘ − x₁ and y₂ = 2·yₘ − y₁. With endpoint A(−1, 4) and midpoint M(3, 1), the other endpoint is B(2×3 − (−1), 2×1 − 4) = (7, −2).

Is the midpoint the same as the average?

Yes. Each coordinate of the midpoint is the arithmetic mean of the two endpoints' coordinates, which is why the midpoint is exactly halfway along the segment.

What is the perpendicular bisector?

It is the line through the midpoint at a right angle to the segment. Every point on it is the same distance from both endpoints. Its slope is the negative reciprocal of the segment's slope.

Can the coordinates be negative or decimals?

Yes. Any real numbers work, including negatives, decimals and zero. Results are shown to up to 6 decimal places.

How do I find a point that divides a segment in another ratio?

Use the section formula: the point a fraction t of the way from A to B is A + t × (B − A) for each coordinate. The table shows t = 0, 0.25, 0.5, 0.75 and 1.

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