📍 Midpoint Calculator
Find the midpoint of two points in 2D or 3D, a missing endpoint, or the point dividing a segment in a ratio — with distance, slope and a graph.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2) = ((2 + 8)/2, (3 + 11)/2)
What Midpoint Calculator Does
This midpoint calculator finds the point exactly halfway between two points, in two or three dimensions, and shows the midpoint formula with your numbers filled in. It also works backwards — give one endpoint and the midpoint to find the missing endpoint — and it can find the point that divides a segment in any ratio, such as one third of the way from A to B.
Alongside the answer you get the length of the segment, half its length and, in 2D, its slope, plus a small graph of the points so you can see the result makes sense. Negative and decimal coordinates are fine.
How to Use Midpoint Calculator
- Choose midpoint, missing endpoint, or point at a ratio
- Tick 3D if your points have z-coordinates
- Enter the coordinates of the points
- Read the result with the formula filled in
- Check the distance, slope and graph
Formula Used by Midpoint Calculator
Midpoint
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
Worked example
A(2, 3) and B(8, 11).
- (2 + 8) ÷ 2 = 5
- (3 + 11) ÷ 2 = 7
Result: M = (5, 7).
Missing endpoint
B = 2M − A
Worked example
A(−1, 4) and midpoint M(3, 1).
- x: 2 × 3 − (−1) = 7
- y: 2 × 1 − 4 = −2
Result: B = (7, −2).
Section formula
P = (n·A + m·B) ÷ (m + n), where AP : PB = m : n
Worked example
A(0, 0), B(9, 6), m : n = 1 : 2.
- x: (2 × 0 + 1 × 9) ÷ 3 = 3
- y: (2 × 0 + 1 × 6) ÷ 3 = 2
Result: P = (3, 2), one third of the way from A.
Related Coordinate Formulas
| Quantity | Formula |
|---|---|
| Distance | d = √((x₂ − x₁)² + (y₂ − y₁)²) |
| Slope | m = (y₂ − y₁) ÷ (x₂ − x₁) |
| Midpoint (3D) | ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2) |
| Perpendicular bisector slope | −1 ÷ m |
How to Read Your Result
Checking your answer
The midpoint should be the same distance from both endpoints, and its coordinates should lie between theirs. If a coordinate of your midpoint is outside the range of the endpoints’ coordinates, a sign has slipped.
Circles and bisectors
The midpoint of a diameter is the circle’s center, and the radius is half the diameter’s length — both shown here. The perpendicular bisector of a segment passes through its midpoint with slope −1/m, which is how you find the set of points equidistant from two points.
Limitations & Accuracy Notes
- The graph is drawn for 2D points only.
- The section formula here finds internal division; external division uses a minus sign in the formula.