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- Finds the midpoint of a line segment from its two endpoints.
- Finds a missing endpoint when you know one end and the midpoint.
- Also shows the segment length, the slope and the perpendicular bisector.
- Shows each step of the midpoint formula.
How to use the midpoint calculator
Choose what to find
The midpoint, or a missing endpoint.
Enter the known points
Both endpoints, or endpoint A and the midpoint M.
Read the answer
See the result with the working and extra details.
The midpoint formula
The midpoint is the point exactly halfway between two endpoints. Its x is the average of the two x values and its y is the average of the two y values.
Midpoint formulas
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
Missing endpoint: x₂ = 2 × Mx − x₁, y₂ = 2 × My − y₁
Example 1: (2, 3) and (8, 7)
Average the coordinates.
- Mx (2 + 8) ÷ 2 = 5
- My (3 + 7) ÷ 2 = 5
- Midpoint (5, 5)
- Segment length 7.211103
Example 2: missing endpoint
A = (2, 3), midpoint M = (5, 5)
- x₂ 2 × 5 − 2 = 8
- y₂ 2 × 5 − 3 = 7
- Endpoint B (8, 7)
Example 3: negative coordinates
(−3, 4) and (5, −2)
- Midpoint (1, 1)
- Segment length 10
Where the midpoint is used
Geometry
Find centres of segments, diagonals and circles.
Perpendicular bisectors
The bisector passes through the midpoint.
Maps
Find a halfway point between two coordinates on a grid.
Design and layout
Centre objects between two positions.
Measure the segment with the distance formula calculator or find its steepness with the slope calculator.
Midpoint calculator FAQ
What is the midpoint formula?
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Average the x values and average the y values.
How do you find a missing endpoint?
Double the midpoint and subtract the known endpoint: x₂ = 2Mx − x₁ and y₂ = 2My − y₁.
What is the midpoint of (2, 3) and (8, 7)?
It is (5, 5).
Can a midpoint have decimals?
Yes. If the sum of the coordinates is odd, the midpoint has .5 in it.
Is the midpoint always on the segment?
Yes. It lies on the segment and splits it into two equal halves.
What is a perpendicular bisector?
A line that crosses the segment at its midpoint at a right angle.