Travel calculators

Magnetic Declination Calculator

Updated Sep 16, 2026 By Infinity Calculator
Rate Formulas

Location Input

Geodetic uses altitude above the ellipsoid; geocentric uses radius from Earth's centre.
Accepts 40.7486, 40°44'55"N, 40:44:55S or 40 44 55 N. Positive = North.
Accepts -73.9864, 73°59'11"W or 73 59 11 W. Positive = East.
Minimum −2,300 km above the ellipsoid.

Interactive Map

Click or tap anywhere on the map to set the coordinates, or drag the marker. With the map focused you can also use the arrow keys (Shift = 10° steps) and press Enter to calculate. Prefer typing? The Latitude and Longitude fields above are a fully equivalent, screen-reader-friendly way to set the same point.

Date, Model & Resolution

Range: 2025–2030
WMM is recommended for navigation; IGRF for research use.
Model resolution
Off = standard (degree 12). On = high resolution (technical / research use).
Magnetic Declination Result
Magnetic declination (D)
—
Secular variation (SV) of declination
—
Location & date used
— —
Full Magnetic Field Components
All components computed from the selected model at the coordinates and date shown above.
ElementValueAnnual change
Declination Drift Over the Model Validity Window
Step-by-Step Solution

Introduction

A compass does not point to true north. It points to magnetic north, which sits in a different spot. The gap between them is called magnetic declination (pilots often call it magnetic variation). This calculator tells you that gap for any place on Earth.

Pick your spot in one of three ways: search for a city, type in latitude and longitude, or just click the map. Then choose a date. The tool uses the World Magnetic Model (WMM2025) or IGRF-14 to work out the answer.

You get the declination in degrees, minutes and seconds, or NATO mils. You also get the full magnetic field: inclination (dip), horizontal and vertical strength, and total strength. A compass rose shows the offset, and a chart shows how it will drift over the next few years.

This matters for flying, sailing, hiking, surveying, and setting up antennas. Runway numbers and chart headings are based on magnetic north, and that north keeps moving. If you know the declination, you can turn a magnetic bearing into a true bearing, or the other way around. The step-by-step math is shown too, so you can check the work or learn how it is done.

How to use our Magnetic Declination Calculator

Give the tool a spot on Earth and a date. It shows you the magnetic declination there (how far a compass needle points away from true north), plus the full magnetic field values, a compass picture, a drift chart, and the math steps.

City / Place Search tab: Type a city, town, or landmark name, then press Search & Place. The tool finds the spot and fills in the coordinates for you.

Country: Pick a country to keep the search inside it. Leave it on "Any country" to search the whole world.

U.S. state / territory: This box shows up only when you choose the United States. Pick a state to narrow the search even more.

Manual Coordinates tab: Use this if you already know the exact spot, like an airport or a waypoint.

Coordinate system: Choose Geodetic (WGS84) for normal maps, charts, and GPS. Choose Geocentric only if you are measuring distance from the center of the Earth.

Latitude: Type how far north or south the spot is. You can write 40.7486, 40°44'55"N, or 40 44 55 N. North is positive, south is negative.

Longitude: Type how far east or west the spot is. You can write -73.9864, 73°59'11"W, or 73 59 11 W. East is positive, west is negative.

Altitude (or Radius): Type your height above the ellipsoid. Use 0 for ground level, or your cruise altitude for flying. Pick the unit next to it: km, m, ft, mi, or nmi.

Interactive Map: Click or tap the map to drop the marker, or drag it. You can also focus the map and use the arrow keys, then press Enter.

Date format: Pick Calendar date to use a normal YYYY-MM-DD date, or Decimal year to type something like 2026.5.

Date (or Decimal year): Enter the day you need the declination for. Stay between 2025 and 2030, or the answer gets less accurate.

Geomagnetic model: Keep WMM2025 for flying, sailing, and charts. Pick IGRF-14 for science and research work.

Model resolution: Leave the switch off for standard resolution, which matches aviation and marine charts. Turn it on for extra detail used in technical work.

Display declination as: After you calculate, choose decimal degrees, degrees/minutes/seconds, or NATO mils to match your charts or gear.

Field intensity unit: Pick nT, µT, mG, or G for the magnetic field strength shown in the components table.

Calculate and Reset: Press Calculate to see your results. Press Reset to clear everything and start over. You can then download the results as JSON or CSV, or copy them to your clipboard.

What Is Magnetic Declination?

A compass needle does not point to true north. It points to magnetic north, which is a spot that moves a little each year. Magnetic declination (also called magnetic variation) is the angle between true north and magnetic north at your exact spot on Earth. If the needle points to the right of true north, the declination is east (a plus number). If it points to the left, it is west (a minus number).

Why Declination Matters

Every map, chart, and GPS route uses true north. Your compass does not. If you ignore the difference, you drift off course. A 5° error grows into about 1 mile of drift for every 12 miles you travel. Pilots, sailors, hikers, and surveyors all correct for it.

In aviation the same angle is called variation. It is printed on aeronautical charts as dashed isogonic lines, and it is why runway numbers are based on magnetic headings, not true headings. Airports repaint and renumber runways when the local variation drifts far enough. Air traffic control headings are magnetic too.

How to Use the Number

  • Magnetic to true: add east declination, subtract west declination.
  • True to magnetic: subtract east declination, add west declination.
  • An old pilot memory trick: "East is least, West is best". Subtract east and add west when going from true to magnetic.

Secular Variation: The Yearly Drift

Earth's magnetic field is made by moving liquid iron in the core, so it slowly changes. This slow change is called secular variation. Declination can shift by a few arcminutes each year in most places. That is why an old chart can be wrong today, and why you should always use a current date when you check declination.

The Models Behind the Numbers

Declination is not measured at every point on Earth. It is calculated from a math model of the whole field:

  • WMM (World Magnetic Model), built by NOAA and the British Geological Survey. It is the standard for aviation, marine, and military navigation, and it is updated every five years.
  • IGRF (International Geomagnetic Reference Field), made by scientists worldwide and mostly used for research.

Both models use a method called spherical harmonic synthesis, which adds up many wave-like terms to rebuild the field at any latitude, longitude, altitude, and date.

Other Field Values You Will See

  • Inclination (I) is how steeply the field dips into the ground. Near the poles it is almost straight down, which makes compasses sluggish and unreliable.
  • Horizontal intensity (H) is the sideways pull that actually turns a compass needle. Low H means a weak, slow needle.
  • X, Y, Z are the north, east, and downward parts of the field.
  • Total intensity (F) is the full strength of the field, usually 25,000 to 65,000 nanotesla.

Things That Can Throw a Compass Off

Declination is only the Earth-wide part of the error. Local iron rock, power lines, car engines, aircraft metal, and electronics cause extra error called deviation. Near the magnetic poles, declination changes fast over short distances and a compass may be nearly useless. The agonic line is the path where declination is exactly zero. Along it, magnetic north and true north line up.

Formulas used

Time-varying Gauss coefficients
g_n^m(t) = g_n^m(t_0) + (t - t_0)\,\dot{g}_n^m, \quad h_n^m(t) = h_n^m(t_0) + (t - t_0)\,\dot{h}_n^m
Geodetic to geocentric conversion
R_c = \frac{a}{\sqrt{1 - e^2\sin^2\phi}},\quad p = (R_c + h)\cos\phi,\quad z = \left(R_c(1-e^2) + h\right)\sin\phi,\quad r = \sqrt{p^2 + z^2},\quad \phi' = \arcsin\!\left(\frac{z}{r}\right)
Spherical harmonic field synthesis (geocentric components)
\begin{aligned} X' &= \sum_{n=1}^{N}\left(\frac{a}{r}\right)^{n+2}\sum_{m=0}^{n}\left(g_n^m\cos m\lambda + h_n^m\sin m\lambda\right)\frac{dP_n^m(\theta)}{d\theta} \\ Y' &= \frac{1}{\sin\theta}\sum_{n=1}^{N}\left(\frac{a}{r}\right)^{n+2}\sum_{m=0}^{n} m\left(g_n^m\sin m\lambda - h_n^m\cos m\lambda\right)P_n^m(\theta) \\ Z' &= -\sum_{n=1}^{N}\left(\frac{a}{r}\right)^{n+2}\sum_{m=0}^{n}(n+1)\left(g_n^m\cos m\lambda + h_n^m\sin m\lambda\right)P_n^m(\theta) \end{aligned}
Rotation to the local horizon frame
\psi = \phi' - \phi,\quad X = X'\cos\psi - Z'\sin\psi,\quad Y = Y',\quad Z = X'\sin\psi + Z'\cos\psi
Magnetic declination and inclination
D = \arctan\!\left(\frac{Y}{X}\right),\qquad I = \arctan\!\left(\frac{Z}{H}\right)
Horizontal and total field intensity
H = \sqrt{X^2 + Y^2},\qquad F = \sqrt{H^2 + Z^2} = \sqrt{X^2 + Y^2 + Z^2}
Secular variation of declination and inclination
\dot{D} = \frac{X\dot{Y} - Y\dot{X}}{H^2},\qquad \dot{I} = \frac{H\dot{Z} - Z\dot{H}}{F^2},\qquad \dot{H} = \frac{X\dot{X} + Y\dot{Y}}{H},\qquad \dot{F} = \frac{X\dot{X} + Y\dot{Y} + Z\dot{Z}}{F}
Decimal year from calendar date
t = Y + \frac{\tau - \tau_{\text{Jan 1},Y}}{\tau_{\text{Jan 1},Y+1} - \tau_{\text{Jan 1},Y}}

Frequently asked questions

Is magnetic north the same as the geographic North Pole?

No. The geographic North Pole is a fixed point where all the lines of longitude meet. The north magnetic pole is where Earth's magnetic field points straight down, and it sits hundreds of miles away from the true pole. Your compass needle lines up with the field, so it points toward the magnetic pole, not the true one. The angle between the two directions at your spot is the magnetic declination.

How fast is the magnetic north pole moving?

It moves every year, and the speed changes. In the early 1900s it crawled along at about 10 km (6 miles) a year. By the early 2000s it sped up to roughly 55 km (34 miles) a year as it left the Canadian Arctic and headed toward Siberia. It has slowed again lately, to about 35 km (22 miles) a year.

Because of this drift, the declination where you live changes too, usually by a few arcminutes each year.

How do I set declination on my compass?

Many baseplate and lensatic compasses have a small screw or a turning ring for declination:

  • Look up the declination for your area first.
  • Use the tiny key (often on the lanyard) to turn the screw until the orienting arrow sits at your declination angle: right of north for east, left of north for west.
  • Now you can read true bearings straight off the compass with no math.

If your compass cannot be adjusted, do the math yourself: add east declination to a magnetic bearing, or subtract west declination, to get the true bearing.

Does my phone compass show true north or magnetic north?

It depends on the setting. The sensor inside your phone measures the magnetic field, but most phones then apply a built-in declination model and display true north by default. iPhones have a "Use True North" switch in Compass settings; many Android compass apps have the same option.

Keep the phone away from magnets, metal cases, speakers, and car dashboards. Those cause errors that no model can fix.

Does GPS use magnetic north or true north?

GPS itself works in true north. It finds your position from satellites, and direction of travel is computed from real positions, not from a magnet.

Many handheld GPS units and aircraft displays then show you a magnetic bearing anyway, because charts, runways, and ATC headings are magnetic. The unit simply applies the declination from a stored model. Check your device's north reference setting so you know which one you are reading.

Why do airports change their runway numbers?

Runway numbers come from the runway's magnetic heading, rounded to the nearest 10 degrees with the last digit dropped. A runway pointing 184° magnetic is Runway 18.

Magnetic north keeps drifting, so over the years that heading slowly changes. When the drift pushes it past the rounding point, the airport has to repaint the numbers, redo the signs, and update the charts. Tampa International did this in 2011, and several Alaska airports have done it too, because declination changes fastest at high latitudes.

Does altitude change magnetic declination?

Yes, but only a little. The magnetic field gets weaker as you go up, and the direction shifts slightly too. At a normal airliner cruise height of about 12 km (39,000 ft), the change in declination is usually well under a tenth of a degree, far too small to matter for a heading.

Altitude matters much more for satellites and high-flying research work, where the field strength drops a lot.

Where on Earth is magnetic declination the biggest?

Near the magnetic poles. Stand close to one and magnetic north can be 90°, or even 180°, away from true north, so the number becomes huge and changes fast over short distances.

In the lower 48 United States the range is much tamer, roughly 15° east in Washington State to about 15° west in Maine. Alaska is more extreme, with values over 20° east in some places.

What is the difference between variation and deviation?

Variation (the same thing as declination) is the Earth-wide error. It depends only on where you are and the date, not on your vehicle.

Deviation is a local error caused by your own gear: engines, steel, radios, wiring, speakers, or a phone in your pocket. It changes with the heading you are flying or sailing.

You fix variation with a model. You fix deviation by moving metal away or by using a deviation card.

What is a compass deviation card?

It is a small card mounted next to the magnetic compass in a plane or boat. It lists the heading you should steer to actually fly or sail a given magnetic heading, for example "For 030 steer 032."

A technician makes the card during a compass swing, lining the vehicle up on a marked compass rose and noting the error at each heading. The card must be redone after big electrical or metal work.

Why do pilots near the poles use true north instead of magnetic?

Two reasons. First, declination changes very fast near the poles, so a magnetic heading can be off badly after only a short distance. Second, the field points almost straight down there, so the sideways pull that turns a compass needle is weak and the needle gets slow and sloppy.

Above roughly 70 to 75° latitude, charts switch to true north, and crews use grid navigation with inertial or GPS systems instead of the magnetic compass.

How often is the World Magnetic Model updated?

Every five years. The current version is WMM2025, and it covers 2025 through 2030. Each release includes yearly change rates so it can predict the field between updates.

Once, in 2019, the field shifted faster than expected and NOAA released an early out-of-cycle update before the normal 2020 version. That is why it pays to check declination with a current date instead of trusting an old chart.

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