Distance Between Two Points Calculator

The Euclidean distance formula calculates the straight-line distance between two points. In 2D: d = √[(x₂ − x₁)² + (y₂ − y₁)²]. In 3D: d = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]. It's derived directly from the Pythagorean theorem.

2D distance works on a flat plane with only x and y coordinates (like points on a map or graph paper). 3D distance adds the z-axis for depth/height, used in physics, engineering, 3D modeling, and real-world measurements where elevation matters. The 3D formula simply adds the squared z-difference under the square root.

Yes! Negative coordinates are fully supported. The formula squares the differences (x₂ − x₁), so negative values become positive automatically. The visual canvas also adapts to show points in all four quadrants (2D) or all eight octants (3D).

Euclidean distance has countless applications: GPS navigation calculates straight-line ("as-the-crow-flies") distance; architects measure spatial relationships; game developers detect collisions; machine learning algorithms (like k-NN) use it for classification; physics uses it for displacement calculations; and it's fundamental in computer graphics and robotics.

Results are displayed to 6 decimal places using JavaScript's 64-bit floating-point arithmetic (IEEE 754), providing accuracy suitable for virtually all practical applications. For extremely large or extremely small numbers, standard floating-point precision limits apply.

No! Distance is symmetric: the distance from A to B equals the distance from B to A. Whether you compute (x₂ − x₁) or (x₁ − x₂), squaring the result makes it positive. Our "swap" button lets you quickly exchange coordinates without changing the calculated distance.

Δx, Δy, and Δz (delta) represent the difference between coordinates: Δx = x₂ − x₁, Δy = y₂ − y₁, Δz = z₂ − z₁. These are the horizontal, vertical, and depth components of the distance. In 2D, the distance is the hypotenuse of a right triangle with legs |Δx| and |Δy|.

Absolutely! This distance calculator is 100% free, requires no sign-up or download, and works directly in your browser. There are no usage limits. It's designed for students, teachers, engineers, and anyone needing quick coordinate geometry calculations.