Calculate true bearing, magnetic bearing, or magnetic declination from any two values in degrees or radians, with East/West sign convention.
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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 = true bearing
- MB = magnetic bearing
- D = magnetic declination
Bearings are normalized to a 0ยฐ to 360ยฐ range. Declination is normalized to a -180ยฐ to +180ยฐ range. If you use radians, the calculator converts values to degrees for the calculation, then converts the result back to radians.
- 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 8.5ยฐ |
| West declination | Magnetic north is west of true north | Negative, such as -8.5ยฐ |
| True bearing | Direction measured from true north | 0ยฐ to 360ยฐ |
| Magnetic bearing | Direction measured from magnetic north | 0ยฐ to 360ยฐ |
Common Direction Angles
| Direction | Degrees | Radians |
|---|---|---|
| North | 0ยฐ or 360ยฐ | 0 or 2ฯ |
| East | 90ยฐ | ฯ/2 |
| South | 180ยฐ | ฯ |
| West | 270ยฐ | 3ฯ/2 |
Quick Examples
If your magnetic bearing is 70ยฐ and the declination is 10ยฐ east, the true bearing is:
70ยฐ + 10ยฐ = 80ยฐ
If your true bearing is 120ยฐ and the declination is 8ยฐ west, enter the declination as -8ยฐ. The magnetic bearing is:
120ยฐ – (-8ยฐ) = 128ยฐ
If the result goes below 0ยฐ or above 360ยฐ, wrap it back into the 0ยฐ to 360ยฐ bearing range.
