Midpoint Calculator
Find the midpoint of a line segment between two points (x₁, y₁) and (x₂, y₂) — averages the x and y coordinates separately.
What is Midpoint Calculator?
The midpoint calculator finds the point exactly halfway between two given points in the coordinate plane. The midpoint is the average of the x-coordinates and the average of the y-coordinates.
Formula
Midpoint formula:
M = ( (x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2 )
It is just the average of each coordinate. The midpoint is equidistant from both endpoints and lies on the segment connecting them.
Worked example
Points (1, 2) and (5, 8):
- M_x = (1 + 5) ÷ 2 = 3
- M_y = (2 + 8) ÷ 2 = 5
- Midpoint = (3, 5)
How to use this calculator
- Enter the coordinates of the two endpoints.
- The midpoint coordinates appear instantly.
Frequently asked questions
When do I use the midpoint formula?
Geometry proofs, finding the center of a line segment for partitioning, dividing a region into halves, computing the center of a circle from two endpoints of a diameter, and any "halfway between" question.
How is it related to the average?
The midpoint is literally the average of two points — coordinate by coordinate. M = average of endpoints.
Does it work in 3D?
Yes — extend with a z-coordinate: M_z = (z₁ + z₂) ÷ 2. This calculator handles 2D.
Is the midpoint always on the line segment?
Yes — it's the unique point that's equidistant from both endpoints and lies on the segment between them.