Distance Calculator

Point 1 Latitude: Point 1 Longitude:

Point 2 Latitude: Point 2 Longitude:

Unit:

Distance in Coordinate Systems

1. 2D Coordinate Plane Distance

The distance between two points (x1,y1)(x1,y1) and (x2,y2)(x2,y2) is calculated using the Euclidean distance formula:d=(x2−x1)2+(y2−y1)2d=(x2−x1)2+(y2−y1)2. Distance Calculator

Key Notes:

The order of points does not affect the result (the formula is commutative).
Example: For (1,5)(1,5) and (3,2)(3,2):d=(3−1)2+(2−5)2=4+9=13d=(3−1)2+(2−5)2=4+9=13

2. 3D Coordinate Space Distance

The distance extends to 3D for points (x1,y1,z1)(x1,y1,z1) and (x2,y2,z2)(x2,y2,z2):d=(x2−x1)2+(y2−y1)2+(z2−z1)2d=(x2−x1)2+(y2−y1)2+(z2−z1)2

Example: For (1,3,7)(1,3,7) and (2,4,8)(2,4,8):d=12+12+12=3d=12+12+12=3

3. Distance on Earth’s Surface

For real-world applications, Earth’s curvature requires spherical or ellipsoidal models. Two common methods:

A. Haversine Formula

Calculates great-circle distance (shortest path on a sphere) between two points given their latitudes (ϕ1,ϕ2)(ϕ1,ϕ2) and longitudes (λ1,λ2)(λ1,λ2):d=2r⋅arcsin⁡(sin⁡2(Δϕ2)+cos⁡ϕ1cos⁡ϕ2sin⁡2(Δλ2))d=2r⋅arcsin(sin2(2Δϕ)+cosϕ1cosϕ2sin2(2Δλ))

rr: Earth’s radius (~6,371 km).
Δϕ=ϕ2−ϕ1Δϕ=ϕ2−ϕ1, Δλ=λ2−λ1Δλ=λ2−λ1 (in radians).
Limitation: ~0.5% error due to Earth’s ellipsoidal shape.

B. Lambert’s Formula

More precise for Earth’s ellipsoid, with ~10-meter accuracy over long distances:d=a(σ−f(X+Yσ))d=a(σ−f(X+Yσ))

aa: Equatorial radius (6,378 km).
σσ: Central angle (computed via auxiliary formulas).
ff: Earth’s flattening (~1/298.257).
X,YX,Y: Terms involving reduced latitudes β1,β2β1,β2.

Note: Both formulas approximate Earth’s irregular surface but are sufficient for most practical purposes.

When to Use Which?

2D/3D Euclidean: Flat geometries (e.g., maps, grids).
Haversine: Spherical Earth models (short-medium distances).
Lambert’s: High-precision or global-scale calculations.

Let me know if you’d like further refinements!