Midpoint Calculator

Find the point halfway between two endpoints in 2D or 3D and verify that both half-segments have equal length.

Calculation inputs

Precision & interpretation

The 2D drawing uses equal axis scales. In 3D mode the diagram is a clearly labeled projection; its on-screen lengths are not 3D distances. Distances are calculated from all three coordinates.

Calculation results

Midpoint M(5, 5)2D · exact coordinate averages

AM3.605551275

MB3.605551275

AB7.211102551

Step-by-step solution

Choose the formula
$M = (\frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2})$
Substitute your inputs
$M = (\frac{2 + (8)}{2}, \frac{3 + (7)}{2})$
Calculate in order
$Average each of the 2 coordinate pairs independently.$
Write the result
$M = (5, 5)$

Segment and midpoint

Both axes use the same scale; each coordinate unit has the same geometric size.

Decimal coordinates are interpreted exactly (up to six decimal places). Diagram coordinates and decimal distances use floating point.

Exact value & calculation details

(5, 5)

Quantity	Value
Point A	(2, 3)
Point B	(8, 7)
Midpoint	(5, 5)
Distance (decimal)	7.211102550927979
Distance (exact)	√(52)

Understand the calculation

Concept & meaning

A midpoint divides a segment in the ratio 1:1. Average each coordinate independently; the same construction extends naturally from two dimensions to three.

Formula & special cases

The midpoint is a location, not a length. Its coordinates can be negative even though each half-segment distance is nonnegative.

Precision & limitations

The 2D drawing uses equal axis scales. In 3D mode the diagram is a clearly labeled projection; its on-screen lengths are not 3D distances. Distances are calculated from all three coordinates.

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

Worked example from your inputs

2D · exact coordinate averages = (5, 5)

Frequently asked questions

Can the midpoint have fractional coordinates?

Yes. Even whole-number endpoints can have a half-integer coordinate.

Is the midpoint the same as distance?

No. The midpoint is a coordinate tuple. Distance is the length between two points.

Does it work in 3D?

Yes. Select 3D to include z₁ and z₂ and calculate the third midpoint coordinate.

What happens if both endpoints are the same?

The midpoint is that same point, and both half-segment distances are zero.

Show all questions (5 more)Show fewer questions

What does the Midpoint calculate?

Find the point halfway between two endpoints in 2D or 3D and verify that both half-segments have equal length.

Which values should I enter?

Use the labeled fields above. Values outside the supported range clear the result and show an explanation.

What formula does this calculator use?

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

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Inputs and presets update the result, teaching diagram and expandable steps together. Invalid input clears the previous result.

Sources & References

$OpenStax official logo$ OpenStax · CoordinatesDistance, midpoint and Cartesian coordinatesRead the reference $OpenStax official logo$ OpenStax · Complex numbersModulus, argument and polar representationRead the reference

References explain the mathematics; they do not imply institutional endorsement.