Midpoint Calculator

Find the midpoint between two coordinate points

Your result will appear here.

About the Midpoint Calculator

The midpoint of two points lies exactly halfway between them in coordinate space. It is useful for geometry, mapping and finding the centre of a line segment.

Because the midpoint is found coordinate by coordinate, it works the same way whether the segment slopes upward, downward or is horizontal or vertical. The method also extends naturally into three dimensions by averaging the z-coordinates as well.

How to Use the Midpoint Calculator

  1. Enter the coordinates of the first point.
  2. Enter the coordinates of the second point.
  3. Calculate the midpoint.
  4. Keep x-values paired with x-values and y-values paired with y-values.

How the Calculation Works

For two-dimensional points (x₁,y₁) and (x₂,y₂), the midpoint is M = ((x₁+x₂)/2, (y₁+y₂)/2). The x-coordinates are averaged together and the y-coordinates are averaged together because the halfway position is determined independently along each axis.

The same idea extends to three dimensions by averaging the z-coordinates as well: ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). This coordinate-by-coordinate averaging places the result at equal straight-line distance from both endpoints.

Worked example

Midpoint Calculator Worked Example

Midpoint of (2,4) and (8,10)

x midpoint = (2+8)÷2 = 5. y midpoint = (4+10)÷2 = 7. The midpoint is (5,7).

Result guide

Understanding Your Midpoint Calculator Result

The midpoint is equidistant from the two endpoints along the straight segment connecting them.

Before you rely on the answer

Assumptions and Limitations

  • Coordinates use the same coordinate system and scale.
  • Points are interpreted in ordinary Cartesian geometry.
  • Units are consistent when coordinates represent physical distances.

Practical tip

Using This Result in Practice

A quick check is that each midpoint coordinate should fall between the corresponding endpoint coordinates unless the endpoints are equal in that axis. If the result is being used in a drawing or map, keep the coordinate scale unchanged; averaging coordinates from different scales would not identify the geometric halfway point.

Related calculations

Useful Calculations to Continue With

If you also need the length of the line segment, use the Distance Between Two Points Calculator.

If you need the line’s direction or rate of change, use the Slope Calculator.

Common questions

Midpoint Calculator FAQ

How do I find a midpoint?

Average the x-coordinates and average the y-coordinates separately.

Can midpoint coordinates be decimals?

Yes. If the sums are not even multiples of 2, one or both midpoint coordinates can be fractional.

Is the midpoint always on the line segment?

Yes, under ordinary Cartesian geometry it lies halfway along the segment joining the endpoints.