Key takeaways
- The midpoint formula is M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
- It averages the x-coordinates and the y-coordinates separately.
- The midpoint always lies exactly on the line segment between the two points.
- Swapping the two points doesn't change the midpoint.
In this guide
What is the midpoint formula?
The midpoint of two points is the point exactly in the middle of the straight line connecting them. You find it by averaging the x-coordinates and averaging the y-coordinates separately.
Why does the midpoint formula matter?
It finds a genuinely fair "halfway" point between two locations, without needing to measure or guess.
Two friends live at (2, 2) and (10, 8) on a city grid. Their fair meeting point is ((2+10)/2, (2+8)/2) = (6, 5) — exactly halfway along the straight line between their homes, not just "somewhere in the middle."The formula
| Symbol | What it means | Example |
|---|---|---|
| M | The midpoint, as an (x, y) pair | (6, 5) |
| (x₁, y₁) | The first point's coordinates | (2, 2) |
| (x₂, y₂) | The second point's coordinates | (10, 8) |
How to find the midpoint step by step
- 1Write down both points' coordinates.
- 2Add the two x-coordinates and divide by 2. This gives the midpoint's x-value.
- 3Add the two y-coordinates and divide by 2. This gives the midpoint's y-value.
- 4Combine both results into the midpoint (x, y).
Now try it yourself. Change the two points in the calculator below and watch the midpoint update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting to divide by 2. Adding the coordinates alone gives double the midpoint value, not the midpoint itself.
- Confusing midpoint with distance. The midpoint is a location halfway between two points; the distance formula gives how far apart they are.
- Assuming order matters. Swapping which point is "first" and "second" never changes the midpoint.
Tips and tricks
- Sanity-check your answer: the midpoint's x-value should always sit between the two original x-values, and the same for y.
- Once you have two points, the distance formula calculator tells you how far apart they actually are.
Where you'll use it in real life
- Meetups: finding a fair meeting point between two friends' locations on a map.
- Geometry: locating the center of a line segment in a diagram.
- Circles: finding the center of a circle from two endpoints of its diameter.
- Design: centering an object exactly between two reference points on a layout.
Quick summary
To find the midpoint between two points, average their x-coordinates and average their y-coordinates separately. The result always sits exactly halfway along the line between them. Use the calculator above to check your own two points instantly.
Worked example
You and a friend live at map coordinates (2, 2) and (10, 8). You want to find a meeting point exactly halfway between your two homes.
- 01M = ((2+10)/2, (2+8)/2)
- 02M = (12/2, 10/2)
- 03M = (6, 5)
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the midpoint if I only know one point and the midpoint?
Rearrange the formula: the missing point's x-coordinate is (2 × midpoint x) - known x, and the same pattern works for the y-coordinate.
Is the midpoint always exactly on the straight line between the two points?
Yes. The midpoint always lies exactly on the line segment connecting the two points, at the halfway mark.
What's the difference between the midpoint formula and the distance formula?
The midpoint formula finds the location halfway between two points. The [distance formula](/calculator/distance-formula) finds how far apart the two points are, as a single length value.
Does the order of the two points change the midpoint?
No. Swapping which point you call point 1 and point 2 gives exactly the same midpoint, since addition doesn't depend on order.
