Coordinates · destination point
Destination point from bearing and distance.
Enter a start point, a true bearing and a distance. Get the latitude and longitude you arrive at by following a great circle.
Inputs
Result
Enter your coordinates.
Finding a point from a bearing and a distance
Travelling a distance d on an initial true bearing θ from (φ1, λ1) along a great circle ends at φ2 = asin(sin φ1 × cos δ + cos φ1 × sin δ × cos θ) and λ2 = λ1 + atan2(sin θ × sin δ × cos φ1, cos δ − sin φ1 × sin φ2), where δ = d / R is the distance as an angle. These are the Aviation Formulary's "lat/lon given radial and distance" equations.
Worked example. Starting at Toronto (43.6532, -79.3832) and travelling 1,000 km on a bearing of 45° ends at 49.6214, -69.5594. Checking that result with the distance and bearing calculators returns 1,000 km, so the two directions agree.
The bearing is the direction you leave on. Following a great circle, the heading changes along the way, so this is not the same as holding a constant compass course; for that, see the rhumb line calculator. The result is wrapped into -180° to 180° longitude.
Frequently asked questions
Which earth radius does this use?
The mean radius of the WGS 84 ellipsoid, 6371.0088 km. Treating the earth as a sphere can differ from an ellipsoidal calculation by up to about 0.3%, so it is right for planning and general use but not for surveying.
Can I type degrees, minutes and seconds?
Yes. Each box accepts decimal degrees (43.6532), degrees and decimal minutes (43 39.19 N) or degrees, minutes and seconds (43°39′11″ N). Use a minus sign or the letters S and W for south and west.
Does the bearing stay constant along the way?
No. This follows a great circle, so only the initial bearing is the one you enter. A constant-heading path is a rhumb line, which is a different route.
What if the distance is larger than half the earth's circumference?
The path continues past the point opposite your start and comes back round. The tool shows a note when this happens.
Sources
Checked
- Ed Williams, Aviation Formulary v1.47
- EPSG Geodetic Parameter Dataset: WGS 84 ellipsoid (EPSG:7030)
- NIST SP 811 (2008), Guide for the Use of the International System of Units: mile and nautical mile
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Scope
Spherical-earth, true-bearing calculation. Not a navigation aid; wind, currents, magnetic declination and terrain are ignored.