This endpoint calculator finds the missing endpoint of a line segment when you know the midpoint and the other endpoint.

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B = 2M − A — the Midpoint Formula, Run Backwards

The forward version lives on our Midpoint Calculator. Part of our Math Calculators collection.

Worked Example (Verified)

  • Midpoint (3, 4), known endpoint (1, 2) (defaults): B = (2×3 − 1, 2×4 − 2) = (5, 6)
  • Vector check: A→M = (2, 2); adding it to M gives (5, 6). The midpoint sits exactly halfway in each coordinate.
  • Negative coordinates are welcome: M = (0, 0), A = (−3, 5) → B = (3, −5), the point reflection through the origin.
  • The same formula works coordinate-by-coordinate in 3D: Bz = 2Mz − Az.

Where This Appears

  • Geometry constructions and coordinate proofs (parallelogram diagonals bisect each other — same reflection).
  • Graphics and game code: extending a segment, mirroring a point, finding a circle’s far side from center and one diameter end.
  • Survey/GIS midpoint records where one marker’s coordinates were lost.
  • Any “given the center, find the other end” problem — circles included, since center = diameter midpoint.

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Frequently Asked Questions

How do you find an endpoint given the midpoint and one endpoint?

Use B = (2Mx − Ax, 2My − Ay). With midpoint (3, 4) and endpoint (1, 2): B = (6 − 1, 8 − 2) = (5, 6). Geometrically, reflect the known endpoint through the midpoint.

Why is the formula 2M − A?

The midpoint is the average: M = (A + B)/2. Multiply by 2 and subtract A: 2M − A = B. Each coordinate is handled independently, so the method works in 2D, 3D and beyond.

Can I find a circle diameter’s other endpoint?

Yes — a circle’s center is the midpoint of every diameter. Enter the center as “midpoint” and the known rim point as the endpoint; the result is the antipodal point on the circle.

What if my points have fractions or decimals?

The formula is plain arithmetic and accepts any real coordinates. Keep fractions exact by doubling and subtracting carefully (2 × ½ − ¼ = ¾); this calculator accepts decimals directly.

Does this work in 3D?

Yes: Bz = 2Mz − Az alongside the x and y equations. This page is the 2D form; apply the identical pattern to the z coordinate when your segment lives in space.

Is this endpoint calculator free?

Yes — free, instant, no sign-up.