Magnetic Declination Calculator
Magnetic declination is the angle between true geographic north and the direction a compass needle points. It varies by location and changes slowly over time. Enter your coordinates, altitude, and date to instantly get the declination, inclination, annual rate of change, and corrected bearings for navigation.
What is magnetic declination?
Magnetic declination is the angle between geographic (true) north and magnetic north at any given point on Earth's surface. True north points toward the geographic North Pole, which is where the Earth's rotation axis exits the surface. Magnetic north is the direction a freely suspended compass needle points, which is determined by the orientation of Earth's internal magnetic field. Because the magnetic field is generated by fluid motion in the outer core rather than fixed geography, the two directions do not line up, and the difference - declination - varies with location and changes slowly over time. A positive (easterly) declination means the compass needle points east of true north. A negative (westerly) declination means it points west. On the agonic line - an irregular curve that runs roughly through the eastern United States and parts of South America, as well as through parts of Asia - the two norths coincide and no correction is needed.
How to correct a compass bearing for declination
The basic rule is: "declination east, compass least (subtract); declination west, compass best (add)." More precisely: To convert a compass (magnetic) bearing to a true (map/GPS) bearing: add easterly declination, or subtract the absolute value of westerly declination. Formula: True = Magnetic + Declination (with east positive, west negative). To convert a true bearing to a compass heading to walk: subtract easterly declination, or add the absolute value of westerly declination. Formula: Compass = True - Declination. For example, in New York City the declination is approximately 12 degrees west. A hiker whose map says to walk on a true bearing of 060 degrees should set their compass to 060 + 12 = 072 degrees magnetic. Conversely, if their compass reads 072 degrees, the true bearing they are walking is 072 - 12 = 060 degrees.
Isogonic lines, agonic lines, and secular variation
Lines connecting points of equal magnetic declination are called isogonic lines. They appear on topographic and aviation charts so that map-readers can quickly find the correction for their area. The zero isogonic line - where the compass needs no correction - is called the agonic line. There are currently two main agonic lines: one passing through the Americas (roughly through the eastern United States), and one running through parts of Asia and Australia. Declination is not constant. It drifts slowly over years and decades due to shifts in the convection pattern of Earth's liquid outer core. This slow change is called secular variation. The rate varies by location but is typically between 0.05 and 0.2 degrees per year. Aviation and survey charts are updated periodically to account for this drift. For recreational navigation a check every five years is usually adequate, but professionals and aviators should always use a dated, authoritative source such as the NOAA/NCEI World Magnetic Model.
What is magnetic inclination (dip)?
Alongside declination, the magnetic field has an inclination, also called dip. Inclination is the angle the field lines make with the horizontal plane. At the geographic poles the field is nearly vertical (inclination close to 90 degrees), and at the magnetic equator it is nearly horizontal (inclination close to 0 degrees). Inclination matters for compass design: a compass built and balanced for use in Europe would dip noticeably if taken to Australia, because the field direction changes. Good quality compasses are built with a counterweight to balance for a specific latitude zone, and global compasses use a freely pivoting needle assembly. Inclination also matters for borehole logging, directional drilling, and magnetometer surveys, where knowing the full 3-D field vector is essential.
Magnetic declination by major city (approx. 2025)
| City | Latitude | Longitude | Approx. Declination | Direction |
|---|---|---|---|---|
| New York, USA | 40.7 N | 74.0 W | 12 deg | West |
| London, UK | 51.5 N | 0.1 W | 0.5 deg | West |
| Sydney, Australia | 33.9 S | 151.2 E | 13 deg | East |
| Tokyo, Japan | 35.7 N | 139.7 E | 8 deg | West |
| Los Angeles, USA | 34.1 N | 118.2 W | 11 deg | East |
| Cape Town, South Africa | 33.9 S | 18.4 E | 26 deg | West |
| Toronto, Canada | 43.7 N | 79.4 W | 10 deg | West |
| Mumbai, India | 19.1 N | 72.9 E | 1 deg | West |
Values are approximate. Always use a current calculator for navigation. East declination means the compass points east of true north.
Frequently asked questions
What is the difference between true north and magnetic north?
True north is the direction toward Earth's geographic North Pole - the point where the rotation axis meets the surface. Magnetic north is the direction a compass needle points, which is controlled by Earth's magnetic field. The two directions differ by an angle called magnetic declination, which can be as large as 25 degrees or more in some locations. Maps and GPS coordinates use true north, while a standard compass points toward magnetic north, so you must apply the local declination to get from one to the other.
Does magnetic declination change over time?
Yes. Earth's magnetic field is generated by fluid motion in the outer core, and that motion shifts slowly over years and decades. As a result, the direction and magnitude of magnetic north change over time - a process called secular variation. The rate is typically 0.05 to 0.2 degrees per year at most locations, though it can be faster near regions of rapid core change. Navigation charts and magnetic models are updated periodically to track these changes. Printed compass roses on older paper maps can be years or decades out of date.
What is the agonic line?
The agonic line is the isogonic line where magnetic declination is zero - that is, where magnetic north and true north point in exactly the same direction. Along the agonic line no compass correction is needed. Currently there are two main agonic lines on Earth: one passes roughly through the eastern United States (and shifts slowly westward over time), and another passes through parts of Asia and the Pacific. If you are located near an agonic line, compass navigation with a map is especially straightforward.
Why does declination differ so much between cities?
Declination depends on your distance from the magnetic poles and on the complex, non-dipole structure of Earth's core field. The field is not a perfect bar magnet: there are regional anomalies caused by magnetised rocks in the crust and by asymmetries in core convection. This means declination can differ by 20 degrees or more between two cities at the same latitude if they are on opposite sides of a magnetic anomaly or on opposite sides of the agonic line.
How accurate is this calculator?
This calculator uses a simplified tilted geocentric dipole model based on the IGRF-13 geomagnetic north pole position. It provides a good first estimate of declination for educational and general navigation purposes, typically accurate to within 2 to 5 degrees of the full World Magnetic Model result. For survey work, aviation, or any safety-critical navigation, use the official NOAA/NCEI World Magnetic Model calculator at ngdc.noaa.gov, which uses the full spherical harmonic expansion and is accurate to within 0.5 degrees.
How do I correct a bearing on a topographic map?
Topographic maps show true north. If your map says walk on a bearing of 045 degrees true and local declination is 10 degrees east, set your compass to 045 - 10 = 035 degrees magnetic, then walk on 035. If declination is 10 degrees west (negative), set your compass to 045 + 10 = 055 degrees magnetic. A simple memory aid: "East is least, west is best" reminds you to subtract east declination and add west declination when converting from true to compass heading.