Calculate true bearing, magnetic bearing, or magnetic declination from any two values in degrees or radians, with East/West sign convention.
Related Calculators
- Line of Sight Calculator
- Barometric Formula Calculator
- Gravity Correction Calculator
- Tidal Range Calculator
- All Physics Calculators
Magnetic Declination Formula
The calculator uses magnetic declination as the angle between true north and magnetic north. East declination is positive. West declination is negative.
TB = MB + D MB = TB - D D = TB - MB
- TB = true bearing
- MB = magnetic bearing
- D = magnetic declination
Bearings are normalized to a 0° to 360° range. Declination is normalized to a -180° to +180° range. If you use radians, the calculator converts values to degrees for the calculation, then converts the result back to radians.
degrees = radians * 180/pi radians = degrees * pi/180
- degrees = angle measured in degrees
- radians = angle measured in radians
- pi = approximately 3.14159
Use a positive value for east declination and a negative value for west declination.
Magnetic Declination Sign and Bearing Rules
| Value | Meaning | How to enter it |
|---|---|---|
| East declination | Magnetic north is east of true north | Positive, such as 8.5° |
| West declination | Magnetic north is west of true north | Negative, such as -8.5° |
| True bearing | Direction measured from true north | 0° to 360° |
| Magnetic bearing | Direction measured from magnetic north | 0° to 360° |
Common Direction Angles
| Direction | Degrees | Radians |
|---|---|---|
| North | 0° or 360° | 0 or 2π |
| East | 90° | π/2 |
| South | 180° | π |
| West | 270° | 3π/2 |
Quick Examples
If your magnetic bearing is 70° and the declination is 10° east, the true bearing is:
70° + 10° = 80°
If your true bearing is 120° and the declination is 8° west, enter the declination as -8°. The magnetic bearing is:
120° – (-8°) = 128°
If the result goes below 0° or above 360°, wrap it back into the 0° to 360° bearing range.
