Bearing Calculator
Our free geography & distance converter handles bearing conversions. See tables, ratios, and examples for quick reference.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Bearing Calculator
Calculator
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Formula: Bearing = atan2(sin(dLon)*cos(lat2), cos(lat1)*sin(lat2) - sin(lat1)*cos(lat2)*cos(dLon))
Worked example — True bearing = ~125.56 deg (SE direction)
Formula
Bearing = atan2(sin(dLon)*cos(lat2), cos(lat1)*sin(lat2) - sin(lat1)*cos(lat2)*cos(dLon))
The bearing formula uses spherical trigonometry to compute the initial direction of the great circle path. The atan2 function handles all quadrants correctly, producing a result normalized to 0-360 degrees. Magnetic bearing is derived by subtracting the local magnetic declination from the true bearing.
Worked Examples
Example 1: Paris to Rome
Problem:Calculate the bearing from Paris (48.8566N, 2.3522E) to Rome (41.9028N, 12.4964E).
Solution:delta_lon = 12.4964 - 2.3522 = 10.1442 deg x = sin(10.1442) * cos(41.9028) = 0.1309 y = cos(48.8566) * sin(41.9028) - sin(48.8566) * cos(41.9028) * cos(10.1442) y = -0.0936 Bearing = atan2(0.1309, -0.0936) = 125.56 deg (SE)
Result:True bearing = ~125.56 deg (SE direction)
Example 2: Magnetic Bearing Correction
Problem:A bearing of 90 degrees true with magnetic declination of -5 degrees (west). What is the magnetic bearing?
Solution:Magnetic bearing = True bearing - Declination Magnetic bearing = 90 - (-5) = 95 degrees When declination is west (negative), magnetic north is west of true north.
Result:Magnetic bearing = 95 degrees
Frequently Asked Questions
What is a bearing in navigation?
A bearing is the direction from one point to another, measured as a clockwise angle from north. True bearing is measured from geographic (true) north, while magnetic bearing is measured from magnetic north. Bearings range from 0 to 360 degrees and are typically expressed as three-digit numbers, such as 045 for northeast or 270 for due west. Bearings are essential in marine navigation, aviation, hiking, surveying, and military operations for determining travel direction.
What is the difference between true bearing and magnetic bearing?
True bearing is measured from geographic north, the fixed point where the Earth's rotation axis meets the surface. Magnetic bearing is measured from magnetic north, which varies by location and changes over time due to shifts in Earth's magnetic field. The difference between them is called magnetic declination (or variation). To convert: magnetic bearing equals true bearing minus declination. If declination is east, subtract it; if west, add it. Declination can range from near zero to over 20 degrees depending on location.
How do I convert between azimuth bearing and quadrant bearing?
Quadrant bearing divides the compass into four quadrants and expresses direction as an angle from north or south toward east or west. For example, azimuth 045 becomes N45E, azimuth 135 becomes S45E, azimuth 225 becomes S45W, and azimuth 315 becomes N45W. To convert from quadrant to azimuth: NxE stays the same, SxE becomes 180 minus x, SxW becomes 180 plus x, and NxW becomes 360 minus x. Quadrant bearings are common in land surveying and legal property descriptions.
What is the final bearing and why does it differ from the initial bearing?
The final bearing is the direction of travel when arriving at the destination, while the initial bearing is the direction when departing. On a great circle route across a sphere, the bearing continuously changes because meridians converge at the poles. For short distances the difference is negligible, but for intercontinental travel it can be significant. The final bearing is calculated by computing the back azimuth from destination to origin and then adding 180 degrees to reverse it.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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