Midpoint Calculator

2D 3D

Point 1

X1:

Y1:

Z1:

Point 2

X2:

Y2:

Z2:

Midpoint Formula: M = ((x1 + x2)/2, (y1 + y2)/2)

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What is a Midpoint?

The midpoint is the exact center point between two given points. It divides a line segment into two equal halves. The midpoint has coordinates that are the average of the corresponding coordinates of the two endpoints.

The Midpoint Formula

2D Midpoint Formula

For two points (x1, y1) and (x2, y2):

M = ((x1 + x2)/2, (y1 + y2)/2)

3D Midpoint Formula

For two points (x1, y1, z1) and (x2, y2, z2):

M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

Understanding the Formula

The midpoint formula simply averages each coordinate:

The x-coordinate of the midpoint is the average of x1 and x2
The y-coordinate of the midpoint is the average of y1 and y2
In 3D, the z-coordinate is the average of z1 and z2

How to Use This Calculator

Select 2D or 3D mode
Enter the coordinates for Point 1
Enter the coordinates for Point 2
Click "Calculate" to find the midpoint

Example Calculations

Example 1: 2D Midpoint

Find the midpoint between (2, 4) and (8, 10):

Mx = (2 + 8) / 2 = 10 / 2 = 5
My = (4 + 10) / 2 = 14 / 2 = 7

Midpoint = (5, 7)

Example 2: Negative Coordinates

Find the midpoint between (-3, 5) and (7, -1):

Mx = (-3 + 7) / 2 = 4 / 2 = 2
My = (5 + (-1)) / 2 = 4 / 2 = 2

Midpoint = (2, 2)

Example 3: 3D Midpoint

Find the midpoint between (1, 2, 3) and (5, 8, 7):

Mx = (1 + 5) / 2 = 6 / 2 = 3
My = (2 + 8) / 2 = 10 / 2 = 5
Mz = (3 + 7) / 2 = 10 / 2 = 5

Midpoint = (3, 5, 5)

Applications of Midpoint

Geometry

Finding centers of line segments, constructing bisectors, and locating centroids of shapes.

Computer Graphics

Calculating center points for animations, positioning objects, and subdivision algorithms.

Navigation

Finding the halfway point between two locations for meeting points or rest stops.

Physics

Calculating center of mass for two-point systems with equal masses.

Related Concepts

Distance Formula: Calculate the length of the line segment
Section Formula: Find any point dividing a segment in a given ratio
Centroid: The "midpoint" concept extended to triangles and polygons