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Geodesy & Distance CalcyZone Calculator

Initial & Final Bearing Calculator

Calculate forward initial compass bearing and reverse final bearing between two geographic coordinates.

📍 Select World Location Presets or Custom Coordinates

WGS-84 Ellipsoid
Point 1 Coordinates (Origin)
Point 2 Coordinates (Destination)
Calculated Geodetic Solution
Initial Bearing: 51.21° | Final Bearing: 108.33°
Forward Initial Bearing51.21°
Reverse / Final Bearing108.33°
🗺️ 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:
  • Start: (40.7128°, -74.006°)
  • End: (51.5074°, -0.1278°)
2. Model & Ellipsoid Reference:WGS-84 / Earth Sphere R = 6,371 km
3. Governing Geodesic Formula:θ = atan2(sin(Δλ)cos(φ2), cos(φ1)sin(φ2) - sin(φ1)cos(φ2)cos(Δλ))
4. Variable Substitution:Initial compass heading from start point towards end point
5. Interpretation & Practical Application:

Departing from point 1 requires an initial true compass heading of 51.21°.

Mathematical Formula

θ = atan2(sin(Δλ)cos(φ2), cos(φ1)sin(φ2) - sin(φ1)cos(φ2)cos(Δλ))

Overview & Explanation

Calculates the initial true compass heading required to depart point 1 along a great circle path.

How It Works

  • Evaluates spherical trigonometry azimuth angles.

Practical Applications

  • Aviation flight planning.
  • Sailing direction headings.

Worked Example: NY to London Bearing

Find departure heading.

1

Compute Bearing

Initial true heading

= Initial Bearing: 51.19° (NE) | Final Bearing: 107.82°

Frequently Asked Questions

Why does bearing change along a great circle?
Great circle paths cross meridians at changing angles, so true compass heading continuously shifts as you travel.

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