Question 1

What is the distance formula?

Accepted Answer

For 2D Cartesian coordinates: distance = √[(x₂−x₁)² + (y₂−y₁)²]. This is an application of the Pythagorean theorem. For 3D: distance = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²].

Question 2

How do I calculate the distance between two GPS coordinates?

Accepted Answer

Use the Haversine formula, which calculates great-circle distance on a sphere: d = 2R × arcsin(√[sin²(Δφ/2) + cos(φ₁)cos(φ₂)sin²(Δλ/2)]), where R = Earth radius (6,371 km), φ = latitude, λ = longitude.

Question 3

What is the difference between Euclidean and Manhattan distance?

Accepted Answer

Euclidean distance is the straight-line ("as the crow flies") distance between two points. Manhattan distance (city-block distance) is the sum of absolute differences in each coordinate: |x₂−x₁| + |y₂−y₁|. Manhattan is used in grid-based navigation and some machine learning algorithms.

Question 4

How accurate is the Haversine formula for geographic distances?

Accepted Answer

Haversine assumes a perfect sphere and has up to 0.5% error for very long distances because the Earth is an oblate spheroid. For most practical purposes, this accuracy is sufficient. The Vincenty formula is more accurate for extreme precision needs.

Question 5

What is the distance formula used for in real life?

Accepted Answer

Common applications: GPS navigation (calculating distances between waypoints), computer graphics (collision detection, ray tracing), logistics (optimizing delivery routes), astronomy (stellar distances), and machine learning (k-nearest neighbor algorithms).

Distance Calculator