What Is the 3D Distance Calculator?
This calculator finds the straight-line (Euclidean) distance between two points located in three-dimensional space. Each point is described by three coordinates — an x value, a y value, and a z value — and the tool returns the shortest distance separating them. It is the natural extension of the familiar 2D distance formula into a third dimension, making it useful in geometry, physics, computer graphics, engineering, and 3D modeling.
How to Use It
Enter the coordinates of the first point (\(\text{X}_1\), \(\text{Y}_1\), \(\text{Z}_1\)) and the second point (\(\text{X}_2\), \(\text{Y}_2\), \(\text{Z}_2\)). Click calculate to see the distance along with the component differences \(\Delta x\), \(\Delta y\), and \(\Delta z\). Coordinates may be positive, negative, or decimal values, and the result is expressed in the same units as your inputs.
The Formula Explained
The distance is computed with the three-dimensional Pythagorean theorem:
$$d = \sqrt{\left(\text{X}_2 - \text{X}_1\right)^2 + \left(\text{Y}_2 - \text{Y}_1\right)^2 + \left(\text{Z}_2 - \text{Z}_1\right)^2}$$
Each axis difference is squared so negatives never reduce the total, the squares are summed, and the square root converts the sum back to a linear measurement. Because the contributions are added under one root, the order of the points does not matter.
Worked Example
Suppose point A = (1, 2, 3) and point B = (4, 6, 3). Then \(\Delta x = 3\), \(\Delta y = 4\), \(\Delta z = 0\). Squaring gives $$9 + 16 + 0 = 25,$$ and \(\sqrt{25} = 5\). The two points are exactly 5 units apart.
FAQ
Does the order of the points matter? No. Swapping point 1 and point 2 only flips the sign of each difference, and squaring removes the sign, so the distance is identical.
What units does the result use? Whatever units your coordinates are in. If you enter meters, the distance is in meters; the formula is unit-agnostic.
What if two points are identical? All differences are zero, so the distance is 0.
