Midpoint Calculator (2D & 3D)

Find the exact midpoint $M$ of a line segment connecting two endpoints, $P_1$ and $P_2$. The midpoint is calculated by finding the average of the coordinates for each dimension ($x, y$, and optionally $z$).

The Midpoint Formula (2D and 3D)

The midpoint formula is a direct application of the arithmetic mean. For each dimension, the midpoint coordinate is simply the average of the two endpoints' coordinates.

Midpoint Formula (2 Dimensions)

Given endpoints $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$, the midpoint $M$ is:

Midpoint Formula (3 Dimensions)

For three dimensions, the formula is extended to include the $z$ coordinate:

The calculation principle remains identical: find the average position along each axis.

Related Formula: Distance Between Two Points

While the midpoint finds the location of the center of the segment, the distance formula finds the length of the segment ($D$). The 2D distance formula is:

Frequently Asked Questions (FAQ)

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M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)

D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

x_2 = 2 M_x - x_1

$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)$

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$