3D Distance Calculator — Distance Between Two Points

Understanding the 3D Distance Formula

The 3D distance formula is the natural extension of the Pythagorean theorem into three dimensions. In two dimensions, the straight-line (Euclidean) distance between two points is found by squaring the horizontal and vertical differences, adding them, and taking the square root. In 3D, we simply include the depth difference as a third squared term.

Consider two points: P₁ = (x₁, y₁, z₁) and P₂ = (x₂, y₂, z₂). The component differences are (x₂ − x₁), (y₂ − y₁), and (z₂ − z₁). The Euclidean distance D between these points is: D = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²).

This formula accepts any real numbers, including negatives and decimals, and is widely used in computer graphics and game development (to measure object separation), physics and engineering (to compute magnitudes of displacement), robotics and path planning (to evaluate shortest paths), GIS and mapping (to estimate straight-line distances), and general spatial analytics.

How This 3D Distance Calculator Works

The tool runs entirely in your browser using JavaScript—no data leaves your device. After you enter x₁, y₁, z₁, x₂, y₂, and z₂ and click “Calculate Distance,” it:

• Parses your inputs as numbers and validates them.
• Computes dx = x₂ − x₁, dy = y₂ − y₁, and dz = z₂ − z₁.
• Squares each component and sums them: dx² + dy² + dz².
• Takes the square root to return the final Euclidean distance.

Results are instantaneous and private, making this calculator ideal for quick checks, coursework, and engineering sketches without leaving traces online.

Common Uses

Computer graphics and games, physics/engineering (displacement), robotics/path planning, and GIS/mapping.