Convert a magnetic bearing to true (or true to magnetic) using your local magnetic declination, or find the declination from two bearings.

Uses a declination you supply, e.g. from a chart or the NOAA model. Correct compass deviation first.

East positive; west negative. Enter โˆ’8 for 8ยฐ W.

Optional settings

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 0ยฐ inclusive through 360ยฐ exclusive. Recovered declination uses โˆ’180ยฐ exclusive through +180ยฐ inclusive; +180ยฐ and โˆ’180ยฐ 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 ร— 180 / pi; radians = degrees ร— 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 8.5ยฐ
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.