Navigation Bearing Calculator
Free Navigation bearing Calculator for adventure outdoor activity. Enter your stats to get performance metrics and improvement targets.
Reviewed by Sher, Sports Science & Nutrition Specialist
Formula
Bearing = atan2(sin(dLon) x cos(lat2), cos(lat1) x sin(lat2) - sin(lat1) x cos(lat2) x cos(dLon))
The forward azimuth formula calculates the initial bearing from point A to point B using spherical trigonometry. Coordinates are converted to radians, the angular difference is computed using arctangent, and the result is normalized to 0-360 degrees. Magnetic bearing adds the local declination. Distance uses the Haversine formula with Earth radius of 6,371 km.
Worked Examples
Example 1: New York to London Bearing
Problem:Calculate the true and magnetic bearing from New York (40.7128N, 74.0060W) to London (51.5074N, 0.1278W) with magnetic declination of -13 degrees.
Solution:Using spherical trigonometry:\nLat1 = 40.7128, Lon1 = -74.0060\nLat2 = 51.5074, Lon2 = -0.1278\ny = sin(73.878) x cos(51.507) = 0.598\nx = cos(40.713) x sin(51.507) - sin(40.713) x cos(51.507) x cos(73.878) = 0.342\nTrue bearing = atan2(0.598, 0.342) = 51.2 degrees\nMagnetic bearing = 51.2 + (-13) = 38.2 degrees\nHaversine distance = 5,570 km
Result:True Bearing: 51.21 deg (NE) | Magnetic: 38.21 deg | Distance: 5,570 km
Example 2: Trail Navigation Bearing
Problem:Calculate bearing from trailhead (46.8523N, 121.7603W) to summit (46.8700N, 121.7400W) with declination +15 degrees.
Solution:Lat1 = 46.8523, Lon1 = -121.7603\nLat2 = 46.8700, Lon2 = -121.7400\ny = sin(0.0203) x cos(46.87) = 0.0096\nx = cos(46.852) x sin(46.87) - sin(46.852) x cos(46.87) x cos(0.0203) = 0.0013\nTrue bearing = atan2(0.0096, 0.0013) = 40.47 degrees\nMagnetic bearing = 40.47 + 15 = 55.47 degrees\nDistance = 2.33 km
Result:True Bearing: 40.47 deg (NE) | Magnetic: 55.47 deg | Distance: 2.33 km
Frequently Asked Questions
What is a navigation bearing and how is it used in outdoor navigation?
A navigation bearing is the angular direction from one point to another, measured clockwise from true north in degrees from 0 to 360. Bearings are fundamental to land navigation, marine navigation, and aviation for determining the direction of travel between two known positions. When hiking, you take a bearing by pointing your compass at a distant landmark and reading the degree value where the direction-of-travel arrow intersects the compass housing. A bearing of 0 or 360 degrees points due north, 90 degrees points east, 180 degrees points south, and 270 degrees points west. Bearings can be expressed as true bearings referenced to geographic north, or magnetic bearings referenced to magnetic north, with the difference between them called magnetic declination.
What is the difference between true bearing and magnetic bearing?
True bearing is measured relative to geographic or true north, which is the direction toward the geographic North Pole and remains constant at any given location. Magnetic bearing is measured relative to magnetic north, the direction a compass needle actually points, which differs from true north because the magnetic pole is located approximately 500 kilometers from the geographic pole and moves over time. The angular difference between true and magnetic north is called magnetic declination, which varies by location from near zero at some points to over 20 degrees in parts of North America and even larger values near the poles. To convert a true bearing to a magnetic bearing, you add the magnetic declination for east declination or subtract for west declination, depending on local convention.
How does the bearing calculation work using latitude and longitude coordinates?
The bearing between two points on Earth is calculated using spherical trigonometry formulas that account for the curved surface of the globe. The forward azimuth formula uses the arctangent of two values: the sine of the longitude difference multiplied by the cosine of the destination latitude, divided by the cosine of the origin latitude times the sine of the destination latitude minus the sine of the origin latitude times the cosine of the destination latitude times the cosine of the longitude difference. This formula produces the initial bearing or forward azimuth, which is the direction you would face if standing at the origin looking toward the destination. Due to the curvature of the Earth, the bearing changes continuously along a great circle path, so the initial bearing differs from the final arrival bearing.
How do I follow a bearing in the field with a compass?
Following a bearing in the field requires converting your calculated true bearing to a magnetic bearing by accounting for local declination, then setting and following that bearing on your compass. First, set the magnetic bearing on your compass housing by rotating the bezel until the desired degree marking aligns with the direction-of-travel arrow. Hold the compass flat and rotate your body until the compass needle aligns with the orienting arrow in the housing, often called putting the red in the shed. The direction-of-travel arrow now points along your desired bearing. Select a visible landmark along that line and walk to it, then repeat the process. In poor visibility, use intermediate landmarks every 50 to 100 meters. On steep terrain, bearings may need adjustment because slope angle effectively changes your horizontal direction of travel.
References
Reviewed by Sher, Sports Science & Nutrition Specialist · Editorial policy