Magnetic Declination Formula
Reference for magnetic declination — the angle between true and magnetic north.
Explains east and west corrections for compass bearings in hiking and sailing.
Need to calculate, not just reference? Use the interactive version.
Open Magnetic Declination Calculator →
The Formula
True Bearing = Magnetic Bearing + Declination
Magnetic declination is the angle between true north (geographic) and magnetic north (where the compass points). It varies by location and changes slowly over time as Earth's magnetic field shifts.
Variables
| Symbol | Meaning |
|---|---|
| True Bearing | Direction relative to true (geographic) north |
| Magnetic Bearing | Direction shown on a magnetic compass |
| Declination | Angle between true north and magnetic north (positive = east, negative = west) |
Example 1
Your compass reads 120° and the local declination is +10° East
True Bearing = 120° + 10°
True Bearing = 130°
Example 2
You need to travel on a true bearing of 45°. Local declination is -15° West.
Magnetic Bearing = True Bearing - Declination
Magnetic Bearing = 45° - (-15°) = 45° + 15°
Set your compass to 60°
When to Use It
Use the magnetic declination formula when:
- Navigating with a magnetic compass in the wilderness
- Converting between map bearings and compass readings
- Calibrating navigation instruments
- Working with nautical or aeronautical charts
Key Notes
- Declination changes over time as Earth's magnetic field slowly drifts — some locations shift more than 1° per decade; always use a current declination value, not one from an old map
- Memory aid: "East is least, West is best" — for east declination, subtract from magnetic bearing to get true; for west declination, add it
- Modern smartphones auto-correct for declination in their navigation apps — but for paper map and compass navigation, manual correction remains essential for precision
Key Notes
- Definition: Magnetic declination is the angle between true (geographic) north and magnetic north at a specific location. It is positive (east) when magnetic north is east of true north, and negative (west) when it is west of true north.
- Varies dramatically by location: Declination ranges from +20° or more in parts of Alaska to −25° in eastern Australia. In central Europe it is currently around +1° to +3°. Even a 5° error in navigation translates to significant positional error over long distances.
- Changes over time: Earth's magnetic field drifts continuously. Declination at a given location can change by 1° or more per decade. Maps published more than a few years ago may show outdated declination. Use the NOAA/IGRF model for current values.
- Correcting compass bearing: True = Magnetic + East declination: A mnemonic: "East is least (subtract from magnetic), West is best (add to magnetic)" or simply True = Magnetic + (positive east, negative west). Apply this correction every time you convert between compass and map bearings.
- Applications: Magnetic declination correction is essential in hiking and wilderness navigation, aviation (sectional charts show isogonic lines), marine navigation, land surveying, and calibrating GPS-integrated compass systems in smartphones and aircraft.