Calculator Inputs
Example Data Table
Use these examples to test the calculator quickly.
| Route | Start Latitude | Start Longitude | End Latitude | End Longitude | Use Case |
|---|---|---|---|---|---|
| New York to Los Angeles | 40.7128 | -74.0060 | 34.0522 | -118.2437 | Long distance route |
| London to Paris | 51.5074 | -0.1278 | 48.8566 | 2.3522 | Regional navigation |
| Sydney to Melbourne | -33.8688 | 151.2093 | -37.8136 | 144.9631 | Southern hemisphere route |
Formula Used
1. Haversine distance
The calculator uses:
a = sin²(Δφ / 2) + cos φ1 × cos φ2 × sin²(Δλ / 2)
and d = 2R × atan2(√a, √(1-a)).
Here, R is Earth radius, φ is latitude, and λ is longitude.
2. Initial bearing
The starting true bearing is:
θ = atan2(sin Δλ × cos φ2, cos φ1 × sin φ2 − sin φ1 × cos φ2 × cos Δλ).
The answer is normalized from 0° to 360°.
3. Rhumb line bearing
The rhumb line uses:
θr = atan2(Δλ, Δψ).
It gives a constant compass direction, unlike a great circle path.
4. Three dimensional estimate
Elevation is included with:
3D distance = √(surface distance² + elevation difference²).
This is a useful approximation for terrain-aware work.
How to Use This Calculator
- Enter the starting latitude and longitude in decimal degrees.
- Enter the destination latitude and longitude in decimal degrees.
- Add elevations in meters when height difference matters.
- Select the output distance unit.
- Choose an Earth radius model or enter a custom radius.
- Add magnetic declination if compass correction is needed.
- Press the calculate button to show results above the form.
- Download the CSV or PDF report for saving and sharing.
Understanding GPS Bearing and Distance
Why GPS Coordinates Matter
GPS coordinates describe a point on Earth with latitude and longitude. Latitude measures north or south position. Longitude measures east or west position. When two points are known, this calculator estimates the bearing and distance between them. It uses spherical navigation formulas. These formulas are common in mapping, surveying, field physics, aviation planning, hiking, and marine routing.
How Bearing Works
Bearing is the direction from the start point to the destination. A true bearing is measured clockwise from true north. A value of 0 degrees points north. A value of 90 degrees points east. The initial bearing can change along a great circle route. This happens because Earth is curved. The calculator also shows the final bearing near the destination.
How Distance Is Estimated
Distance is found with the haversine formula. It works well for short and long routes. The method uses latitude, longitude, and Earth radius. You can select kilometers, miles, nautical miles, or meters. You can also include elevation difference. That gives a simple three dimensional path estimate. It is useful when terrain height matters.
Great Circle and Rhumb Line
A rhumb line result is also included. A rhumb line keeps a constant compass direction. It is not always the shortest path. Great circle distance is usually shorter on a sphere. Still, rhumb bearings are practical for some navigation tasks. Comparing both values helps explain the physics of movement across a curved surface.
Midpoint and Central Angle
The midpoint output gives a useful checkpoint. It is the halfway point on the great circle path. The central angle explains the angular separation between the two positions. Smaller angles mean nearby points. Larger angles mean longer arcs across the globe.
Accuracy Tips
Use clean coordinate data for best results. Decimal degrees are the easiest format. North latitudes are positive. South latitudes are negative. East longitudes are positive. West longitudes are negative. Check signs carefully before calculating. A wrong sign can move a point across the world. Use the chart to inspect the route visually. For higher accuracy, choose a radius model that matches your task. The mean radius suits general work. The equatorial and polar values show Earth shape effects. Custom radius settings support planetary demonstrations, classroom experiments, and simplified local navigation checks. Always record source datum too.
FAQs
1. What is bearing in GPS navigation?
Bearing is the direction from one coordinate to another. It is measured clockwise from true north. A bearing of 90 degrees points east, while 180 degrees points south.
2. What is the difference between initial and final bearing?
Initial bearing is the direction at the start point. Final bearing is the direction as the route reaches the destination. They can differ on curved Earth paths.
3. Why does the calculator use the haversine formula?
The haversine formula handles curved surface distance well. It is stable for short routes and long routes. It is widely used for GPS distance estimation.
4. What does rhumb line distance mean?
A rhumb line follows a constant compass bearing. It is simple for navigation, but it may be longer than the great circle route between distant points.
5. Should I enter coordinates in decimal degrees?
Yes. This calculator accepts decimal degrees. Use positive values for north and east. Use negative values for south and west.
6. What is magnetic declination?
Magnetic declination is the angle between true north and magnetic north. This tool subtracts east-positive declination from true bearing to estimate magnetic bearing.
7. Does elevation change affect the result?
Elevation does not change surface distance. It is used only for the simple three dimensional estimate, which combines surface distance with height difference.
8. Can I use a custom planet radius?
Yes. Select the custom radius option and enter the radius in kilometers. This is useful for physics lessons, simulations, and planetary calculations.