Midpoint Calculator
Find the midpoint between two points in 2D or 3D. Enter coordinates to see the midpoint, distance and a step-by-step calculation.
Midpoint formula and example
A midpoint divides a straight line segment into two equal lengths. Find it by averaging each pair of corresponding coordinates. Use the same coordinate system and measurement units for both endpoints.
For A = (2, 3) and B = (8, 11), the midpoint is ((2 + 8) ÷ 2, (3 + 11) ÷ 2) = (5, 7). The pair (5, 7) gives the midpoint’s x- and y-coordinates, not a distance. The endpoints are 10 units apart, and the midpoint is 5 units from either one.
Check an endpoint using the midpoint
Rearranging the midpoint formula gives x₂ = 2mₓ − x₁ and y₂ = 2mᵧ − y₁. If A is (2, 3) and M is (5, 7), the other endpoint is (10 − 2, 14 − 3) = (8, 11). Enter A and this endpoint above to check that their midpoint is M. This is a coordinate calculation, not a travel or driving-distance calculation.
Finding a midpoint in 3D
Select 3D and enter the z-coordinate of each point. Average the z values in the same way as x and y. For (0, 0, 0) and (2, 4, 6), the midpoint is (1, 2, 3).
Distance uses the square root of the sum of the squared coordinate differences. In 2D, this is √((x₂ − x₁)² + (y₂ − y₁)²). In 3D, add (z₂ − z₁)² inside the square root.
Reference: OpenStax: Distance and Midpoint Formulas.
Common questions
Can a midpoint have negative coordinates?
Yes. Average the signed coordinates as entered. The midpoint of (−6, 2) and (2, −4) is (−2, −1).
What happens if the points are identical?
Their midpoint is that same point, and the distance is zero. Swapping different endpoints also leaves their midpoint unchanged.
Can I find a meeting point between two cities?
This formula is for flat Cartesian coordinates. Averaging latitude and longitude does not reliably give a geographic midpoint or a practical meeting place, especially across the date line.
Questions about a result? See how our calculators are built or report a calculation issue.