3D Distance Calculator

Calculate the straight-line distance between two points in a 3D coordinate system. The distance between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by the formula: $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$.

Point 1 (x1):

Point 1 (y1):

Point 1 (z1):

Point 2 (x2):

Point 2 (y2):

Point 2 (z2):

Result:

Understanding the 3D Distance Formula

The 3D distance formula is an extension of the Pythagorean theorem. To find the distance between two points in 3D space, we first find the distance in the XY-plane and then use that result with the Z-axis difference to find the final distance.

Given two points, $P_1 = (x_1, y_1, z_1)$ and $P_2 = (x_2, y_2, z_2)$, the formula works by considering a right-angled triangle where the hypotenuse is the distance, $D$. The legs of this triangle are the distance between the two points in the XY-plane and the difference in their Z-coordinates.

The Pythagorean theorem, $a^2 + b^2 = c^2$, becomes: $(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2 = D^2$

Solving for $D$ gives us the distance formula: $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

How This Tool Works

This tool operates entirely within your browser using JavaScript. When you click "Calculate Distance," it retrieves the six coordinate values you've entered. It then performs the following steps:

Parses the input values as numbers.
Calculates the difference between the x, y, and z-coordinates.
Squares each difference.
Adds the three squared differences together.
Takes the square root of the sum to find the final distance.

All calculations are performed client-side, ensuring your data remains private and is never sent to a server.