Softonic

Midpoint Calculator

Step 1 / 3 Midpoint
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The midpoint between two points is the point whose coordinates are the averages of the two endpoints’ coordinates. Enter (x1, y1) and (x2, y2) for 2D, or add z-values for 3D, and the calculator returns the midpoint, the distance between the two points, and the slope of the line segment connecting them (useful when the midpoint is a step toward a perpendicular bisector problem).

How the midpoint is computed

  1. 1

    Enter point A

    (x1, y1) for 2D, (x1, y1, z1) for 3D.

  2. 2

    Enter point B

    (x2, y2) or (x2, y2, z2) with matching dimension.

  3. 3

    Read the midpoint

    Average the coordinates: ((x1+x2)/2, (y1+y2)/2, ...).

  4. 4

    Read distance and slope

    Distance via the distance formula; slope from rise over run.

The formula

2D midpoint:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

3D midpoint:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2, (z₁ + z₂) / 2)

It’s just the mean of each coordinate treated independently.

Worked examples

2D: A = (2, 3), B = (8, 7).

  • x-midpoint: (2 + 8) / 2 = 5
  • y-midpoint: (3 + 7) / 2 = 5
  • M = (5, 5)

3D: A = (1, 2, 3), B = (7, 4, 11).

  • x: (1 + 7) / 2 = 4
  • y: (2 + 4) / 2 = 3
  • z: (3 + 11) / 2 = 7
  • M = (4, 3, 7)

Related quantities the tool also shows

Distance between the two points:

2D: d = √((x₂−x₁)² + (y₂−y₁)²)

3D: d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)

Slope (2D only):

slope = (y₂ − y₁) / (x₂ − x₁)

Vertical line (x₁ = x₂) has undefined slope.

Where midpoints come up

  • Geometry homework. Finding the center of a line segment; step in constructing a perpendicular bisector or a median of a triangle.
  • Coordinate geometry proofs. Showing a figure is a parallelogram or that diagonals bisect each other.
  • Physics. Center of mass of two equal point masses; halfway point of a trajectory.
  • Game development. Lerping between two positions at t = 0.5 gives the midpoint.
  • GIS and mapping. Approximating “between two places” for location-picker UI.

For more than two points

Midpoint is the mean of two points. For the centroid of three or more points, average all the coordinates:

Centroid = ((x₁ + x₂ + ... + xₙ) / n, (y₁ + ... + yₙ) / n, ...)

Same idea, applied across all points.

Sign and quadrant notes

The midpoint can land in a different quadrant than either endpoint when signs cancel. Example: A = (−3, 2), B = (3, −4). Midpoint = (0, −1), on the axis and below y=0. Always keep signs in mind; the calculator handles negatives correctly.

Frequently Asked Questions

Not directly with this formula, latitude/longitude are spherical coordinates. Averaging lat and lon works OK for points within a few kilometers but fails across long distances (especially near the poles or across the International Date Line). Use a great-circle midpoint formula for distances over a few hundred km.

Convert to Cartesian first: x = r·cos(θ), y = r·sin(θ). Midpoint the Cartesians, then (optionally) convert back to polar.

Yes, the midpoint lies exactly halfway along the straight line between A and B. It’s on the segment by definition.

It doesn’t directly. The midpoint bisects a line segment, not an angle. To bisect an angle, you use angle-bisector constructions involving equal-length rays from the vertex.

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