geo-distance Verified Precision Tool

Rhumb Line / Loxodrome Distance Calculator

Calculate constant-bearing rhumb line (loxodrome) distance and navigational course angle between coordinates.

📍 Select World Location Presets or Custom Coordinates

WGS-84 Ellipsoid

Origin Location Preset

Destination Location Preset

Point 1 Coordinates (Origin)

Latitude (°N/S)

Longitude (°E/W)

Point 2 Coordinates (Destination)

Latitude (°N/S)

Longitude (°E/W)

Calculated Geodetic Solution

5,570.23 km (3,461.179 miles)

Kilometers5570.23 km

Miles3461.179 miles

Nautical Miles3007.685 NM

🗺️ Interactive Geographic Map & Geodesic Trajectory

Click anywhere on the map or drag pins to update coordinates live.

Map Data: © OpenStreetMap ContributorsWGS-84 Precision Geodesic Curve

Step-by-Step Mathematical Derivation

1. Given Input Coordinates:

Origin: (40.7128°, -74.006°)
Destination: (51.5074°, -0.1278°)

2. Model & Ellipsoid Reference:WGS-84 / Earth Sphere R = 6,371 km

3. Governing Geodesic Formula:Haversine Great Circle Formula

4. Variable Substitution:R = 6,371 km

5. Interpretation & Practical Application:

Straight line geodesic distance is 5570.23 km.

Mathematical Formula

Rhumb distance = sqrt(Δlat² + q² * Δlng²) * R, where q = Δlat / ΔΨ

Overview & Explanation

Calculates path distance when following a constant compass course (rhumb line/loxodrome).

How It Works

Projects coordinates onto Mercator isometric latitude space ΔΨ.

Practical Applications

Marine navigation.
Sailing path calculation without constant bearing changes.

Worked Example: Constant Bearing Voyage

Calculate rhumb line path.

Compute Rhumb Distance

Constant course 78.4°

= 5,781 km (slightly longer than great circle)

Frequently Asked Questions

What is a rhumb line?

A rhumb line (loxodrome) is a path that crosses all meridians at the same constant compass angle.

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