Hong Life CalculatorsUnderstanding the magnetic declination calculator — concept and principle
This calculator gives the magnetic declination, the angle between true north and magnetic north, for any location, height and date from 2025 to 2029, using the World Magnetic Model 2025. It also converts a true bearing to a magnetic one and shows the inclination, field components, annual change and whether a compass is reliable there.
How it is calculated
- The World Magnetic Model 2025 (NOAA NCEI and British Geological Survey) describes the main field with spherical-harmonic coefficients up to degree 12, each changing linearly with time from epoch 2025.0.
- Your position on the WGS 84 ellipsoid is converted to geocentric coordinates and the field components X (north), Y (east) and Z (down) are summed.
- H = √(X² + Y²); F = √(H² + Z²); declination D = atan2(Y, X); inclination I = atan2(Z, H).
- Magnetic bearing = true bearing − D. East declination is positive, west negative.
The principle
Earth's magnetic field comes mainly from currents in the liquid outer core. Its magnetic poles do not coincide with the geographic poles, and the field shape is irregular, so a compass needle points away from true north by an amount that varies from place to place. The field also drifts slowly, so declination changes from year to year. The World Magnetic Model fits satellite and observatory data and is updated every five years.
Worked example
Default inputs: latitude 37.5665°, longitude 126.978° (Seoul), sea level, 10 Nov 2026 (decimal year 2026.858), true bearing 45°.
- The model gives X = 29,386 nT, Y = −4,667 nT, Z = 41,953 nT.
- D = atan2(−4,667, 29,386) = −9.02°, so magnetic north is west of true north.
- Magnetic bearing = 45 − (−9.02) = 54°.
- H = 29,754 nT; F = 51,433 nT; inclination = 54.65°.
- Annual change −2.3′/yr; compass reliability: normal compass use.
| Latitude (°, north +, south −) | Magnetic declination (°, east +, west −) |
|---|---|
| 9.39 | -1.87 |
| 18.8 | -3.95 |
| 28.2 | -6.37 |
| 37.6 | -9.02 |
| 47 | -11.76 |
| 56.3 | -14.49 |
| 75.1 | -20.21 |
How to read the result
With a west declination, add its size to a true bearing to get the magnetic bearing; with an east declination, subtract it. Typical model error is about 0.3–0.5°, larger near the magnetic poles and wherever iron, steel, power lines or local rocks distort the field. Where H falls below 6,000 nT the model flags a caution zone, and below 2,000 nT compasses are unreliable.
Common mistakes
- Applying the correction with the wrong sign.
- Using an old map's printed declination without updating it for the annual change.
- Taking readings near cars, steel structures or electronics.
Frequently asked questions
Why does declination change over time?
Flows in Earth's core slowly change the field, so magnetic north drifts.
How often is the model updated?
The World Magnetic Model is released for five-year periods; WMM2025 covers 2025 to 2029.
What is inclination?
The angle the field makes with the horizontal; it is steep near the magnetic poles.
Sources: NOAA NCEI and British Geological Survey, World Magnetic Model 2025 (WMM_2025.COF) · A. Chulliat et al., "The US/UK World Magnetic Model for 2025–2030: Technical Report", NOAA NCEI (2025)