Earth Magnetic Field Declination Estimator
Estimate magnetic declination at any site using a simplified dipole-approximation bearing to the geomagnetic north pole.
🧭 What is Magnetic Declination?
Magnetic declination is the angle between true (geographic) north and the direction a compass needle points (magnetic north) at a given location on Earth's surface. It is positive when magnetic north lies east of true north and negative when it lies west, and its value changes both from place to place and slowly over time as Earth's magnetic field evolves.
Navigators, surveyors, and orienteers use declination to convert between compass (magnetic) bearings and true bearings on a map. Pilots and mariners rely on official declination values to correctly interpret compass headings against charted courses. Geophysics students use simplified dipole models like the one on this page as a first introduction to how Earth's magnetic field is approximated before studying the full, much more complex spherical-harmonic models used in operational navigation. Solar panel installers and satellite dish technicians sometimes need approximate declination to align equipment relative to true south or true north rather than magnetic readings.
A common point of confusion is treating the geomagnetic pole and the north magnetic pole as the same thing. The geomagnetic pole is the point where the axis of Earth's best-fit dipole approximation intersects the surface, and it drifts slowly and fairly predictably. The north magnetic pole is where the real, non-dipole magnetic field actually points straight down, and in recent decades it has moved considerably faster and less predictably, currently tracking toward Siberia. This calculator uses the more stable geomagnetic pole location.
This calculator computes the leading-order dipole approximation to magnetic declination, the initial great-circle bearing from a site to the geomagnetic north pole, the model traditionally taught before higher-order harmonics are introduced. It is useful for building intuition about how declination varies with location, but it is not a substitute for an authoritative real-world magnetic model, a caveat repeated throughout this page because the dipole estimate can diverge substantially from reality in some regions.
📐 Formula
Why this matters, read before trusting a real-world reading: this dipole approximation is a simplified, first-order model. Earth's real magnetic field has substantial non-dipole components, so the actual declination at a given site can differ from this estimate by 10 to 20 degrees or more, particularly across North America. For any real-world navigation, surveying, or engineering decision, use NOAA's official World Magnetic Model (WMM) calculator instead of this educational estimator.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — New York, USA (Large Dipole-Model Divergence)
φ = 40.7128°, λ = -74.0060°, default pole (80.7°N, 72.7°W)
Example 2 — Sydney, Australia (Reasonably Close Estimate)
φ = -33.8688°, λ = 151.2093°, default pole (80.7°N, 72.7°W)
Example 3 — Reykjavik, Iceland (High Latitude, Large Magnitude)
φ = 64.1466°, λ = -21.9426°, default pole (80.7°N, 72.7°W)
❓ Frequently Asked Questions
🔗 Related Calculators
What is magnetic declination?
Magnetic declination is the angle between true (geographic) north and magnetic north as indicated by a compass at a given location. It's positive when magnetic north is east of true north and negative when it's west, and it varies by location and slowly over time.
What formula does this calculator use?
It computes the dipole-approximation great-circle bearing from a site to the geomagnetic north pole using D = atan2(sin(dLambda)cos(phi_p), cos(phi)sin(phi_p) - sin(phi)cos(phi_p)cos(dLambda)), where phi and lambda are the site's latitude and longitude, phi_p and lambda_p are the geomagnetic pole's coordinates, and dLambda is the pole's longitude minus the site's longitude.
Is this calculator's result the same as my real compass declination?
No, and this is an important caveat. This is a simplified educational dipole model. Earth's real magnetic field has substantial non-dipole components, so actual declination can differ from this estimate by 10 to 20 degrees or more in some regions, particularly North America. Always use NOAA's World Magnetic Model (WMM) for real-world accuracy.
Where does the default geomagnetic pole location come from?
The default, 80.7 degrees North, 72.7 degrees West, is an approximate current location of the geomagnetic north pole (the best-fit dipole axis), which drifts slowly and is much more stable than the faster-moving north magnetic pole. You can override both pole coordinate fields to experiment.
What's the difference between the geomagnetic pole and the magnetic north pole?
The geomagnetic pole is where the axis of Earth's best-fit dipole model intersects the surface, and it drifts slowly and fairly predictably. The north magnetic pole is where the real, non-dipole magnetic field points straight down, and it has moved considerably faster and less predictably in recent decades, currently tracking toward Siberia.
Why does this calculator let me change the pole coordinates?
Making the geomagnetic pole position an editable, visible input rather than a hidden constant lets you see directly how sensitive the dipole-model declination is to the assumed pole location, and keeps the model's key simplifying assumption transparent rather than buried.
Why is declination positive in some places and negative in others?
Sign depends on whether the great-circle bearing to the geomagnetic pole points slightly east or west of true north from a given site, which flips depending on the site's longitude relative to the pole's longitude and how far the site is from the pole.
What is the World Magnetic Model (WMM)?
The WMM is the official, regularly updated spherical-harmonic model of Earth's magnetic field jointly produced by NOAA and the British Geological Survey, and it is the authoritative source for real declination values used in aviation, navigation, and surveying, unlike the simplified dipole approximation used by this calculator.
Does magnetic declination change over time?
Yes, both the geomagnetic pole and the real magnetic field drift over years and decades due to changes in Earth's core dynamics, so declination at a fixed location slowly changes too. Official models like the WMM are updated every five years to track this secular variation.
How do I use declination to convert a compass bearing to true north?
Add easterly (positive) declination to a magnetic bearing to get true bearing, or subtract westerly (negative) declination. For example, with +10 degrees declination, a compass reading of 90 degrees magnetic corresponds to 100 degrees true.