How to use it
- Choose a place: search, use your location, or click the map.
- Set the date and, if it matters, the height above sea level.
- Read the declination and the other elements. The orange line on the map points to magnetic north, the dashed grey line to true north.
5 practical uses
- Correct a compass bearing for a map, or a map bearing for a compass.
- Set the declination on a handheld compass or a GPS unit.
- Check an old map's declination note against today's value.
- Align a telescope, a sundial or a survey baseline to true north.
- Understand why a phone compass and a paper map disagree.
The maths behind it
The World Magnetic Model describes the Earth's main field as a spherical harmonic expansion of degree 12: the potential is V = R Σ (R/r)ⁿ⁺¹ Σ (gₙᵐ cos mλ + hₙᵐ sin mλ) Pₙᵐ(cos θ), with 168 Gauss coefficients and their yearly changes. The page evaluates the field components X (north), Y (east) and Z (down) from the gradient of V at the place and date, then declination = atan2(Y, X), inclination = atan2(Z, √(X²+Y²)) and the total field F = √(X²+Y²+Z²).
Reading the numbers
- Declination (also called variation): the angle from true north to magnetic north. To turn a map bearing into a compass bearing, subtract an east declination or add a west one.
- Inclination (dip): the angle the field makes with the horizontal, down in the northern hemisphere, up in the southern; 90° at the magnetic poles.
- Total field and its horizontal and vertical parts, in nanotesla. Near the magnetic poles the horizontal part is tiny and a compass is useless.
- Annual change: how the declination moves in a year; the model carries this so old maps can be corrected.
The model
The World Magnetic Model is produced by NOAA's NCEI and the British Geological Survey for the US and UK defence departments, and is the model built into phones, aircraft and ships. WMM2025 is valid from late 2024 to late 2029; outside that range the tool still computes, but the error grows. Local iron, power lines and the metal of a car add anomalies the model cannot know about.