Magnetic Declination Inclination From Coordinates Calculator
Calculate magnetic declination with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
tan(I) = 2cos(theta)/sin(theta); D = arctan(sin(phi_m - phi) / (cos(lat)tan(lat_m) - sin(lat)cos(phi_m - phi)))
Magnetic inclination I is calculated from the geomagnetic co-latitude theta using the dipole formula. Declination D is derived from spherical trigonometry relating geographic and magnetic pole positions. These are simplified dipole approximations; real-world values require the full IGRF model with higher-order spherical harmonics.
Worked Examples
Example 1: Navigation in New York City
Problem:Find the magnetic declination and inclination for New York City (40.7128 N, 74.0060 W) at sea level in 2025.
Solution:Using the dipole model:\nLatitude: 40.7128 N, Longitude: 74.0060 W\nGeomagnetic co-latitude calculated from magnetic north pole (80.65 N, 72.68 W)\nDeclination: approximately -12 to -13 degrees (west)\nInclination: approximately 67-68 degrees (downward dip)\nTotal field intensity: approximately 52,000 nT
Result:Declination: ~12-13 degrees West | Inclination: ~67-68 degrees | Compass reads ~12 degrees east of true north
Example 2: Expedition Planning in Australia
Problem:Determine magnetic parameters for Sydney, Australia (-33.8688 S, 151.2093 E) for a hiking expedition.
Solution:Using the dipole model:\nLatitude: 33.8688 S, Longitude: 151.2093 E\nSouthern hemisphere location gives negative inclination\nDeclination: approximately 12-13 degrees (east)\nInclination: approximately -64 degrees (upward tilt in southern hemisphere)\nTotal field intensity: approximately 57,000 nT
Result:Declination: ~12-13 degrees East | Inclination: ~-64 degrees | Subtract ~12-13 degrees from compass reading for true north
Frequently Asked Questions
What is magnetic declination and why does it matter?
Magnetic declination (also called magnetic variation) is the angle between true north (geographic north) and magnetic north as indicated by a compass. This angle varies depending on your location on Earth because the magnetic poles do not coincide with the geographic poles. Declination is measured in degrees east or west of true north. If declination is 10 degrees east, your compass needle points 10 degrees east of true north. This matters critically for navigation because failing to account for declination can lead to significant positional errors. At a distance of 10 kilometers, a 10-degree error puts you approximately 1.7 kilometers off course, which can be dangerous in wilderness navigation, aviation, and maritime operations.
What is magnetic inclination or dip angle?
Magnetic inclination, also called magnetic dip, is the angle between the horizontal plane and the direction of the Earth's magnetic field lines at a given location. At the magnetic equator, the field lines are parallel to the Earth's surface, so the inclination is zero degrees. At the magnetic poles, the field lines point straight down into the Earth, giving an inclination of plus or minus 90 degrees. In the northern hemisphere, the north end of a compass needle dips downward (positive inclination), while in the southern hemisphere it tilts upward (negative inclination). Understanding inclination is important for geophysical surveys, mineral exploration, drilling operations, and calibrating electronic compasses. Inclination also affects the accuracy of magnetic compasses at high latitudes where the field becomes nearly vertical.
How does the Earth's magnetic field change over time?
The Earth's magnetic field is constantly changing due to complex fluid motions in the outer core, a phenomenon called secular variation. The magnetic north pole has been drifting from northern Canada toward Siberia at an accelerating rate, currently moving roughly 40-55 kilometers per year. Magnetic declination at any given location can change by several degrees over decades. For example, declination in London has changed from about 11 degrees east in 1580 to 24 degrees west in 1820 and back to about 1 degree west currently. The International Geomagnetic Reference Field (IGRF) model is updated every five years to account for these changes. Long-term records show the field has weakened by about 10 percent over the last 150 years, though complete reversals occur on geological timescales.
How do I correct a compass reading for magnetic declination?
To convert a magnetic compass bearing to a true bearing, add east declination or subtract west declination. The mnemonic 'East is least, West is best' helps remember this: for east declination, subtract from the true bearing to get magnetic (or add to magnetic to get true). For example, if declination is 12 degrees east and your compass reads 45 degrees, the true bearing is 45 + 12 = 57 degrees. If declination is 8 degrees west and your compass reads 200 degrees, true bearing is 200 - 8 = 192 degrees (but watch the sign: subtracting west means adding a negative, so 200 + (-8) = 192). Many modern compasses have adjustable declination settings that allow you to set the local declination once and read true bearings directly.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy