Select true bearing, magnetic bearing, or magnetic declination as the missing value, then enter the other two in degrees or radians. East declination is positive and west negative.

Bearings are clockwise from north. Declination is east positive, west negative. This bearing relation does not predict local declination from location or date; compass deviation must already be corrected.

East positive; west negative. Use −8 for 8° west.

Related 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. It uses supplied bearings or declination and does not model local declination from a location or date. Correct compass deviation before using a compass reading as magnetic bearing.

TB = MB + D; MB = TB - D; D = TB - MB
  • TB = true bearing
  • MB = magnetic bearing
  • D = magnetic declination

Bearings are normalized to 0° inclusive through 360° exclusive. Recovered declination uses −180° exclusive through +180° inclusive; +180° and −180° represent the same half-circle offset. 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.