Distance Formula (3D)

📊 beginner

$$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$$

Calculates the straight-line distance between two points in three-dimensional space.

Variables & Units

$x, y, z$

Coordinates

Unit: Length units

Key Information

📐 Derived From

Extension of the Pythagorean theorem to three dimensions.

💡 Example

Distance between $(0,0,0)$ and $(1,2,2)$ is $3$.

🔧 Applications

Computer graphics, robotics, and flight path calculations.

⚠️ Constraints

Valid in Euclidean space.

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