Education
Midpoint Formula Calculator
Enter the coordinates of two points and we compute the point exactly halfway between them. The result shows the midpoint as an ordered pair, the x and y components separately, and a step-by-step breakdown using your numbers.
Coordinates
Enter two points (x₁, y₁) and (x₂, y₂).
e.g. 2
e.g. 4
e.g. 8
e.g. 10
Step by step
- 1. Identify the coordinates. x₁ = 2, y₁ = 4, x₂ = 8, y₂ = 10.
- 2. Add the x coordinates. 2 + 8 = 10.
- 3. Divide by 2 for the x of the midpoint. 10 / 2 = 5.
- 4. Add the y coordinates. 4 + 10 = 14.
- 5. Divide by 2 for the y of the midpoint. 14 / 2 = 7.
- 6. Write the midpoint as an ordered pair. M = (5, 7).
M =
(5, 7)
Halfway between (2, 4) and (8, 10)
The midpoint formula M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) averages the x-coordinates and the y-coordinates separately. The result is the point that lies exactly halfway along the straight line between the two inputs.
Examples
(2, 4) and (8, 10)
M = (5, 7)
(0, 0) and (10, 10)
M = (5, 5)
(−4, 6) and (2, −2)
M = (−1, 2)
(1.5, 2.5) and (4.5, 6.5)
M = (3, 4.5)
How it works
For any two points (x₁, y₁) and (x₂, y₂) on a coordinate plane, the midpoint between them is:
Midpoint · M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
The midpoint is the average of the two x-coordinates paired with the average of the two y-coordinates. It lies exactly halfway along the straight line connecting the two points. For the length of that line (rather than its center), see the distance formula calculator.
Frequently asked questions
The midpoint formula is M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2). It returns the point exactly halfway between two given points (x₁, y₁) and (x₂, y₂) on a 2D coordinate plane. The midpoint is the average of the two x-coordinates paired with the average of the two y-coordinates.
Add the two x-coordinates and divide by 2. That gives you the x-coordinate of the midpoint. Add the two y-coordinates and divide by 2. That gives you the y-coordinate. Write the result as an ordered pair (x, y).
The midpoint is the single point that lies exactly halfway along the straight line connecting the two original points. It is the geometric center of the segment. Both points are the same distance from the midpoint, in opposite directions.
Yes. If the two coordinates do not add up to even numbers, the midpoint coordinates will include decimals. For example, the midpoint of (1, 2) and (4, 5) is (2.5, 3.5). That is fine and expected.
Yes. Negative coordinates are fine on either or both points. The formula adds the two coordinates regardless of sign and divides by 2. For example, the midpoint of (−4, 6) and (2, −2) is (−1, 2).
No. They answer different questions. The midpoint is the point halfway between two points (a coordinate pair). The distance is how far apart the two points are (a single number, the length of the line segment). The distance formula calculator handles distance directly.
Yes. The four coordinate fields accept decimals and negative numbers. The result is computed in full floating-point precision and the displayed midpoint coordinates are rounded for readability.
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