Calculating destination...
Enter a start coordinate, bearing, and distance above to calculate the destination point.
What Is the Forward Geodetic Problem?
The forward geodetic problem asks a simple but powerful question: given a starting coordinate on Earth, a direction (bearing), and a distance, where do you end up? Solving it is essential for maritime navigation, aviation route planning, search-and-rescue operations, drone waypoint generation, and any GIS workflow that needs to project a point along a great-circle path.
Our destination point calculator uses the great-circle forward formula derived from spherical trigonometry. It treats the Earth as a sphere with a mean WGS84 authalic radius, giving sub-percent accuracy for most practical navigation and surveying tasks while remaining fast enough to run instantly in a web form.
How to Calculate a Destination Coordinate from Bearing and Distance
To use the calculator, enter the start latitude and longitude in decimal degrees, the true bearing in degrees clockwise from north, and the distance in your preferred unit. The tool converts everything to radians, applies the forward geodetic formula, normalises the destination longitude to the −180° to +180° range, and returns the final coordinate.
The underlying equations are:
φ₂ = asin(sin φ₁ · cos δ + cos φ₁ · sin δ · cos θ)
λ₂ = λ₁ + atan2(sin θ · sin δ · cos φ₁, cos δ − sin φ₁ · sin φ₂)Here, φ is latitude, λ is longitude, θ is the true bearing, and δ is the angular distance (distance divided by Earth radius). The destination longitude is then wrapped into the standard geographic range so results are always map-ready.
Great-Circle vs. Rhumb-Line Navigation
A great-circle route is the shortest path between two points on a sphere. It is why long-haul flights cross polar regions and why trans-oceanic shipping lanes follow curved arcs on flat maps. This calculator solves the great-circle forward problem, so the bearing you enter is the initial bearing at the start point; the path itself will curve unless the bearing is exactly 0°, 90°, 180°, or 270°.
A rhumb line, by contrast, maintains a constant compass bearing and appears as a straight line on a Mercator projection. Rhumb lines are simpler to steer but are longer than great-circle routes for most city pairs. Use this calculator when you need the shortest geodesic path; use a rhumb-line calculator when you need a constant steering bearing.
Earth Radius and Distance Unit Reference
| Unit | Earth Radius | Common Use |
|---|---|---|
| Kilometres (km) | 6 371.0088 | GIS, aviation, general science |
| Miles (mi) | 3 958.7614 | Road distances, US navigation |
| Nautical Miles (nm) | 3 440.065 | Maritime and aviation charts |
| Metres (m) | 6 371 008.8 | Surveying, engineering layout |
Frequently Asked Questions
What is the formula for destination point from bearing and distance?
The great-circle forward formula converts the start coordinate and bearing to radians, computes the angular distance from distance ÷ Earth radius, then uses arcsine and arctangent to derive the destination latitude and longitude. The result is wrapped into the −180° to +180° longitude range.
How do I calculate a destination coordinate in Excel?
Use Excel's RADIANS, DEGREES, ASIN, ATAN2, SIN, and COS functions. Convert latitude, longitude, and bearing to radians, compute angular distance = distance / 6371.0088, then apply the forward formulas shown above. Wrap the final longitude with MOD(lon+540,360)-180.
What is the difference between true bearing and magnetic bearing?
True bearing is measured clockwise from geographic north. Magnetic bearing is measured from magnetic north, which shifts over time and location due to geomagnetic declination. This calculator uses true bearing; add or subtract local magnetic declination if your compass reads magnetic.
When should I use great-circle navigation instead of rhumb line?
Use great-circle navigation when you want the shortest distance between two points on Earth, especially over long ocean or air routes. Use a rhumb line when you need a constant compass heading, such as coastal piloting or simple chart plotting.
How accurate is the haversine forward formula?
The haversine formula assumes a spherical Earth, so accuracy is typically within 0.5% of the geodesic distance computed by WGS84 ellipsoid algorithms like Vincenty. For most navigation, flight planning, and GIS visualisation tasks, this is more than sufficient.
Can I use this for aviation and maritime route planning?
Yes. The calculator is ideal for initial route sketches, waypoint generation, and bearing-distance checks. For certified navigation or flight plans, always cross-check with official charts, NOTAMs, and ellipsoid-based geodetic software.
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