geo-distance Verified Precision Tool
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 EllipsoidPoint 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 point5. 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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