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Bearing Calculator

Calculate compass bearings between GPS coordinates, convert bearing formats, find back bearings, and apply magnetic declination corrections.

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Point-to-Point
Back Bearing
Converter
Magnetic

Enter decimal coordinates (e.g. 51.5074, -0.1278). Negative latitude = South; negative longitude = West.

Point A (Origin)
Point B (Destination)

The back bearing (reciprocal bearing) is the opposite direction — exactly 180° from the original bearing. Used to retrace a route or verify an approach.

Quick Reference
ForwardBackCardinal
000° N180° SNorth → South
045° NE225° SWNE → SW
090° E270° WEast → West
135° SE315° NWSE → NW
180° S000° NSouth → North

Convert a bearing between decimal degrees, degrees/minutes/seconds (DMS), and compass notation.

Input Format
Decimal °
DMS
Compass

Magnetic declination is the angle between true north (geographic) and magnetic north. It varies by location and changes over time.

Easterly declination (+) → magnetic north is east of true north → subtract from true bearing.
Westerly declination (−) → magnetic north is west of true north → add to true bearing.
Find your local declination at ngdc.noaa.gov.
N E S W NE SE SW NW
16-Point Compass
N · 000°
NNE · 023°
NE · 045°
ENE · 067°
E · 090°
ESE · 112°
SE · 135°
SSE · 157°
S · 180°
SSW · 202°
SW · 225°
WSW · 247°
W · 270°
WNW · 292°
NW · 315°
NNW · 337°
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About This Tool

Bearing Calculator computes the compass bearing between two GPS coordinates, converts between bearing formats (decimal degrees, DMS, compass notation), finds reciprocal back bearings, and applies magnetic declination corrections. Includes a live animated compass rose.

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How to Use

  1. Point-to-Point: Enter decimal lat/lng for both points and click Calculate.
  2. Back Bearing: Enter a forward bearing to get its 180° reciprocal.
  3. Converter: Paste a bearing in any format and choose the input type to convert to all others.
  4. Magnetic: Enter a true bearing and your local declination to get the magnetic bearing.
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Logic & Algorithm

Forward bearing uses the Haversine-based azimuth formula: θ = atan2(sin(Δλ)cos(φ2), cos(φ1)sin(φ2)−sin(φ1)cos(φ2)cos(Δλ)). Distance uses the Haversine formula on a spherical Earth (R = 6,371 km). DMS↔decimal uses modulo arithmetic. Magnetic correction subtracts easterly (positive) or adds westerly (negative) declination from the true bearing.

Tags: #Math #Navigation #Bearing #Compass #GPS #Azimuth #Haversine #MagneticDeclination #Free

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From the Blog

Navigation
How to Read a Compass: Bearings Explained
Understand true north, magnetic north, forward bearings, and back bearings with clear examples.
Navigation
What Is Magnetic Declination and Why Does It Matter?
Learn how declination shifts over time and how to apply corrections to your navigation calculations.
GPS
GPS Coordinates Explained: Decimal vs DMS
A practical guide to understanding and converting latitude/longitude coordinate formats.

Frequently Asked Questions

What is a compass bearing?
A compass bearing is an angle measured clockwise from north (0°) to the direction of travel, expressed in degrees from 000° to 360°. North is 000°, East is 090°, South is 180°, West is 270°. It is used in navigation, surveying, and orienteering to describe direction precisely.
What is the back bearing (reciprocal bearing)?
The back bearing is the exact opposite direction of a given bearing — simply add 180° (and subtract 360° if the result exceeds 360°). If your forward bearing from A to B is 045°, the back bearing from B to A is 225°. It is useful for retracing a route or confirming your position.
What is the difference between true north and magnetic north?
True north is the direction toward the geographic North Pole. Magnetic north is where a compass needle points — the magnetic north pole — which is currently located in northern Canada and moves several kilometres per year. The angle between them is called magnetic declination. GPS bearings use true north; compass needles point to magnetic north.
How accurate is the point-to-point bearing calculation?
The calculator uses the Haversine formula on a spherical Earth model (R = 6,371 km), which gives bearing accuracy to within a fraction of a degree for most practical purposes. For very short distances (under 1 km) or polar regions, the error may be slightly larger. The distance result is typically accurate to within 0.3% compared to the WGS84 ellipsoid model.
What is DMS format?
DMS stands for Degrees, Minutes, Seconds. It breaks a decimal angle into whole degrees, whole minutes (1° = 60 minutes), and seconds with decimals (1 minute = 60 seconds). For example, 45.75° = 45° 45' 0". DMS is commonly used in aviation charts, paper maps, and traditional navigation.