Midpoint Formula Calculator
Find the midpoint between two coordinate points. Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). Also calculates the distance and slope of the line segment connecting the two points.
∑ Algebra📐 M = ((x₁+x₂)/2, (y₁+y₂)/2)🔢 Math
x₁
y₁
x₂
y₂
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Midpoint Formula Calculator | — | M = ((x₁+x₂)/2, (y₁+y₂)/2) | coordinate point |
Step-by-Step Examples
Example 1
Basic
(2,4) and (8,10).
- Mx=(2+8)/2=5
- My=(4+10)/2=7
- Midpoint: (5,7)
✓ Midpoint = (5, 7)
Example 2
Negative Coords
(−3,−1) and (5,7).
- Mx=(−3+5)/2=1
- My=(−1+7)/2=3
- Midpoint: (1,3)
✓ Midpoint = (1, 3)
Example 3
Find Missing Endpoint
Midpoint (3,5), one endpoint (1,2). Find other endpoint.
- 2×3−1=5, 2×5−2=8
- Other endpoint: (5,8)
✓ Other endpoint = (5, 8)
Real-World Applications
Geometry
Find center of a line segment or circle diameter.
Data
Average position of two data points in coordinate space.
Navigation
Find exact center point between two GPS locations.
Gaming
Calculate spawn point between two player positions.
Common Mistakes to Avoid
⚠️
Averaging wrong pairs
The x-midpoint uses x1 and x2 only. Do not mix x and y coordinates.
⚠️
Finding endpoint from midpoint
Use endpoint = 2×midpoint − known endpoint. Not just midpoint + difference.
⚠️
3D midpoint
For 3D: M = ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2).
Frequently Asked Questions
What is the midpoint formula? ▾
Midpoint = ((x1+x2)/2, (y1+y2)/2). Simply the arithmetic mean of the x-coordinates and y-coordinates.
How to find an unknown endpoint? ▾
If midpoint M and one endpoint A are known: B = 2M − A. For each coordinate: x_B = 2×M_x − x_A.
What is the perpendicular bisector? ▾
The line passing through the midpoint and perpendicular (slope = −1/original slope) to the segment.
How does the midpoint relate to averages? ▾
The midpoint IS the average position. In higher dimensions, this generalizes to the centroid.
What is a midsegment? ▾
A segment connecting midpoints of two sides of a triangle. It is parallel to the third side and exactly half its length.
Related Math Calculators
Formula Explorer connections
Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.