Stoner Physics

Compass and magnetism

Earth’s magnetic field strength at your location

Earth’s magnetic field is between about 22 and 67 microtesla at the surface, and the figure where you are depends on the place, the height and the year. This calculator evaluates the World Magnetic Model 2025 for any point: total strength in µT and nT, the dip angle, every component and how fast each is changing. It also gives the range a phone’s magnetometer should read there, and checks a reading you enter against it.

Magnetic field strength and dip angle calculator

Enter a position in decimal degrees, or let your device supply it. The model runs in your browser from NOAA’s published WMM2025 coefficients; nothing you enter is sent anywhere by this page. The calculator opens on Casper, Wyoming at zero height, dated today.

Where and when
Check your phone’s reading (optional)

If your app shows three axes instead, enter all three in the same unit; they are used in place of the total.

What it assumes. Earth’s main field only: WMM2025 to degree and order 12, valid 1 January 2025 to 31 December 2029, and no value is given outside that window. It contains no magnetised rock, no daily variation and no magnetic storms (see the limits below). The date is taken at 00:00 UTC. The model wants height above the WGS 84 ellipsoid, which is the height the location button fills in; NOAA’s own calculator also accepts height above sea level, and a 100 m difference moves the total field by about 3.5 nT at most, under a hundredth of the 0.6 µT resolution Android requires of a phone. The ± column is NOAA’s one-standard-deviation error model. The phone range assumes a calibrated reading taken away from steel, magnets and electrical current, does not include error in the phone’s own calibration, and is explained further down. The code reproduces NOAA’s published WMM2025 test values — seven elements and their rates of change at twelve test points, 168 numbers — to the printed precision.

What a phone magnetometer should read

Android reports the magnetic field in microtesla along three axes fixed to the phone: x to the right, y up the screen, z out of the front of the screen (Android SensorEvent documentation). Turning the phone moves Earth’s field from one axis to another but does not change its length, so the total, √(x² + y² + z²), is what to compare with the model, whichever way the phone is held. Every figure in this table comes from the calculator above, for 21 September 2026 at zero height:

PlaceTotal F (µT)Phone range (µT)DipH (µT)Z (µT)
Casper, WY52.548.0 to 57.068.1°19.648.7
Seattle, WA52.648.1 to 57.168.8°19.149.0
New York, NY50.846.2 to 55.365.5°21.046.2
Los Angeles, CA45.941.4 to 50.458.7°23.839.3
Houston, TX46.041.5 to 50.558.3°24.139.1
Miami, FL42.838.3 to 47.353.8°25.334.5
Anchorage, AK54.950.4 to 59.474.0°15.252.8
London, UK49.144.6 to 53.666.5°19.645.1
Singapore42.137.6 to 46.6−12.8°41.1−9.3
Sydney, Australia57.052.5 to 61.5−64.4°24.6−51.4
Hobart, Australia61.957.4 to 66.4−72.6°18.5−59.1
São Paulo, Brazil22.818.3 to 27.3−40.9°17.2−14.9

H is the horizontal part of the field, the only part a compass can use; Z is the vertical part, positive downwards. Across the whole surface, the model’s weakest total field on that date is 22.0 µT, over northern Argentina (26.06° S, 60.49° W), and its strongest is 66.9 µT, over the Southern Ocean between Australia and Antarctica (59.62° S, 134.29° E), found by searching a half-degree grid and refining. That agrees with the British Geological Survey’s statement that total intensity at the surface varies from 22,000 nT to 67,000 nT. One microtesla is 1,000 nanotesla, or 10 milligauss; the whole range is 0.22 to 0.67 gauss.

Use the calibrated reading

Android’s Compatibility Definition Document (CDD, section 7.3.2) requires a device with a 3-axis magnetometer to support online calibration and compensation of the hard-iron bias — the steady offset from magnetised parts inside the phone — and to have soft-iron compensation applied. Android’s sensor documentation says the standard magnetic field readings have temperature compensation, factory or online soft-iron calibration and online hard-iron calibration applied. That calibrated reading is the one to check. The “uncalibrated” magnetometer, which the CDD strongly recommends phones also offer, does not apply the hard-iron calibration; it reports the estimated bias separately. The CDD allows any hard-iron offset under 700 µT (it recommends under 200 µT); 700 µT is more than ten times Earth’s strongest field.

The same section sets the floor on quality: a resolution of 0.6 µT or finer, a range of at least ±900 µT on each axis before saturating, and a standard deviation, per axis, of no more than 1.5 µT over at least 3 seconds of samples at the fastest rate (it recommends 0.5 µT).

Where the phone range comes from

The range is built from the two differences between a clean reading and the model that have published sizes. The model has its own error: 138 nT, or 0.138 µT, one standard deviation for total intensity in NOAA’s error model. The sensor has noise, which Android allows to reach 1.5 µT per axis. Together:

σ = √(0.138² + 1.5²) = 1.506 µT    range = F ± 3σ = F ± 4.52 µT

Three standard deviations is a convention, not a measurement: for normally distributed noise, a reading lands outside it by chance 0.27% of the time. The width is set by the worst noise Android permits. A better sensor, or an average of many samples, is quieter, so a good phone near the edge of the range is already telling you something.

The range leaves one thing out: error in the phone’s own calibration. The CDD requires hard-iron and soft-iron calibration but sets no figure for how accurate the result must be, so there is no published number to put in. A phone whose calibration is off by a few microtesla can land outside the range with nothing magnetic nearby, which is why the check lists calibration among the possible causes.

How the field is calculated

The World Magnetic Model (WMM) describes the part of Earth’s field generated in the core, which NOAA’s National Centers for Environmental Information (NCEI) says accounts for over 95% of the field strength at the surface. WMM2025 was released on 17 December 2024 and expires on 31 December 2029. NCEI records it as produced by the United States’ National Geospatial-Intelligence Agency and the United Kingdom’s Defence Geographic Centre, and developed jointly by NCEI and the British Geological Survey. NCEI states that the information and software may be used freely by the public.

Away from its sources the field is the negative gradient of a scalar potential, and the WMM writes that potential as a sum of spherical harmonics:

V(φ′, λ, r, t) = a Σn=1..12 Σm=0..n [ gnm(t) cos(mλ) + hnm(t) sin(mλ) ] (a/r)n+1 P̄nm(sin φ′)    B = −∇V

a is the magnetic reference radius, 6371.2 km; r, φ′ and λ are radius, geocentric latitude and longitude; P̄nm are the Schmidt semi-normalised associated Legendre functions. To degree and order 12 there are 168 Gauss coefficients g and h, each with a rate of change, and time enters in a straight line from the 2025.0 epoch:

gnm(t) = gnm + ġnm (t − 2025.0)   and the same for h

The calculator follows the step-by-step procedure in section 5.3 of the WMM technical report. The edition opened for this page is the one for WMM2005 (McLean and others, 2004); NCEI’s report for WMM2025 is linked from its WMM page. What shows that this procedure, fed the WMM2025 coefficients, is the WMM2025 calculation is the next section: it reproduces NCEI’s published test values.

  1. Convert the geodetic latitude φ and height h you entered into geocentric latitude φ′ and radius r on the WGS 84 ellipsoid, semi-major axis 6378.137 km and semi-minor axis 6356.7523142 km.
  2. Move each coefficient to the date, as above.
  3. Differentiate the potential to get the north, east and down components X′, Y′, Z′ in the geocentric frame, and the same sums with the rates in place of the coefficients for their changes per year.
  4. Rotate back to the local, geodetic frame through ψ = φ′ − φ: X = X′cosψ − Z′sinψ, Y = Y′, Z = X′sinψ + Z′cosψ.
  5. Everything else follows from those three:

H = √(X² + Y²)    F = √(H² + Z²)    I = arctan(Z / H)    D = arctan(Y / X)    dF/dt = (X·dX/dt + Y·dY/dt + Z·dZ/dt) / F

The report takes the arctangents in the correct quadrant, so declination runs from −180° to 180° and inclination from −90° to 90°, and it notes that declination is undefined where H is zero. Inclination, also called dip, is the angle between the field and the horizontal, positive when the field points down (BGS, The Earth’s Magnetic Field: An Overview): positive in the northern magnetic hemisphere, negative in the southern.

Checked against NOAA’s published test values

NCEI publishes twelve test points for WMM2025, at 2025.0 and 2027.5, at zero and 100 km above the ellipsoid, each with X, Y, Z, H, F, I and D and the rate of change of each — 168 numbers, computed in double precision. This calculator reproduces all 168 to the printed precision; before rounding, every intensity is within 0.05 nT of the printed value and every angle within 0.005°. Four of the rows:

PointF (nT)H (nT)Z (nT)ID
2025.0, 0 km, 80° N 0° E55,178.56,523.254,791.583.21°1.28°
2025.0, 0 km, 0° 120° E41,064.339,677.9−10,580.2−14.93°−0.16°
2025.0, 0 km, 80° S 240° E54,698.216,898.1−52,022.5−72.00°68.78°
2027.5, 100 km, 80° S 240° E51,825.715,927.0−49,317.7−72.10°67.93°

The published and calculated figures are identical in every cell, so the table shows one set. To see it yourself, enter the first row: latitude 80, longitude 0, height 0, date 1 January 2025. The rates match as well; at 80° N 0° E the total field is changing by +30.1 nT a year, as published.

A mid-latitude point: Casper, Wyoming

NOAA’s test points sit at the equator and at 80°, so a mid-latitude check is worth having. The British Geological Survey runs the same model as a web service, which reports whole nanotesla. For Casper (42.8666° N, 106.3131° W) at zero height on 21 September 2026 it gives X = 19,378 nT, Y = 2,896 nT and Z = 48,682 nT. Put through the formulas:

H = √(19,378² + 2,896²) = 19,593.2 nT
F = √(19,593.2² + 48,682²) = 52,477.0 nT
I = arctan(48,682 / 19,593.2) = 68.077°

The service’s own figures are H = 19,593 nT, F = 52,477 nT and I = 68.077°, and it gives the total field as falling by 120.4 nT a year. This calculator gives 19,593.2, 52,477.1, 68.08° and −120.4 nT a year. At five more points (Sydney on the model’s last day, São Paulo, 85° N 130° W in the Arctic blackout zone, Miami at 400 km and 10° N 20° E at 850 km) every intensity agrees with the service to within 1 nT, the step it prints in, and every angle to within 0.001°.

So a calibrated phone lying on a desk in Casper, clear of metal, should read 52.5 µT, and anything from 48.0 to 57.0 µT is within the noise range.

What a reading can and cannot prove

A magnetometer measures the sum of every field present, and fields add as vectors: Bmeasured = Bearth + Bstray. The model supplies the length of Bearth but not its direction in the phone’s axes — that direction is exactly what a compass is trying to find. Two conclusions follow without it.

The strength alone. Two sides of a triangle can differ in length by no more than the third, so the stray field is at least the difference in strength:

|Bstray| ≥ | |Bmeasured| − F |

Strength and dip. With the phone flat and face up, its z axis points straight up, so the three axes also give the measured dip, Im = arctan(−z / √(x² + y²)). Only the compass direction of the measured field is then unknown, and the smallest stray field consistent with both numbers is the one found by swinging the two fields to the same direction:

|Bstray| ≥ √( Bm² + F² − 2 Bm F cos(Im − I) )

The calculator reports that minimum and compares it with the ±4.52 µT noise range. (With the dip included, the minimum is built from two noisy numbers instead of one, so noise alone crosses the same line about 1% of the time rather than 0.27%.) Above it, something besides Earth’s main field is in the measurement: steel, a magnet or an electrical current nearby, magnetised rock, or a phone whose calibration is off. For the compass heading, a level stray field of strength b is worst when it lies at right angles to the field it produces, where it turns the heading by arcsin(b / H); once b reaches H, it can turn it by any amount.

The reverse does not hold: a reading inside the range does not prove there is no interference. A level stray field at right angles to magnetic north is also at right angles to Earth’s whole field, so it adds to the strength only in quadrature, √(F² + b²). At Casper it has to reach 22.2 µT before the total leaves the range, and a field that strong turns the heading by arctan(22.2 / 19.6) = 48.6°. The same field tips the dip from 68.1° to 58.7°, which is what the dip check is for. A surface 1° off level moves the measured dip by up to 1°, worth 0.92 µT of apparent stray field at Casper, so level the phone before trusting a small difference. The magnetic interference page works through how large the heading error is for any stray field and how quickly it falls with distance.

Limits of the model

Main field only. NCEI states that the WMM describes only the long-wavelength part of Earth’s internal field, generated mainly in the fluid outer core, and that the effects of the crust and upper mantle, the ionosphere and the magnetosphere are not represented. The WMM2005 technical report lists what produces spatial anomalies on land: mountain ranges, ore deposits, ground struck by lightning, geological faults, and cultural features such as trains, planes, tanks, railroad tracks and power lines. NCEI adds that declination anomalies can exceed 10°, and that 3 or 4° is not uncommon. For a sense of scale: turning Casper’s 19.6 µT horizontal field by 10° takes a level field of at least 19.6 × sin 10° = 3.4 µT, comparable to the ±4.5 µT phone range.

Time of day and storms. The model has no daily cycle. On magnetically quiet days, BGS gives the regular daily variation at its Hartland observatory as a few tens of nanotesla in total intensity, about 0.1% — well inside a phone’s noise. Magnetic storms are not modelled either, and NCEI says the WMM should not be used during a G5 event, the top of the G0 to G5 storm scale it uses.

Uncertainty. NCEI’s error model gives one standard deviation, including both errors in the coefficients and the parts of the field the model leaves out, as 137 nT for X, 89 nT for Y, 141 nT for Z, 133 nT for H, 138 nT for F, 0.20° for inclination, and √(0.26² + (5417 / H)²) degrees for declination, with H in nT. NCEI describes these as the one-standard-deviation difference between a hypothetical measurement and the calculator result for a location. The calculator prints them beside every value.

Near the magnetic poles. NCEI defines a blackout zone where H is below 2,000 nT, in which compasses are not accurate and should not be relied on for navigation, and a caution zone from 2,000 to 6,000 nT. The total field there is strong, not weak — 57.0 µT at 85° N 130° W in March 2028 — but almost all of it points down. The calculator flags both zones. At the geographic pole itself it gives the strength and dip but no declination, since there is no north to measure it from.

Dates and heights. Nothing is given before 1 January 2025 or after 31 December 2029. NCEI’s calculator takes heights from −1 to 850 km, and so does this one. Height is above the WGS 84 ellipsoid, which is what a browser’s location reports: the W3C Geolocation specification defines its altitude in metres above that ellipsoid.

Running the check live

Bearing, our Android compass, runs the strength half of this check continuously. About twice a second it takes the length of the calibrated magnetometer vector, shows it beside the strength Android’s built-in geomagnetic model predicts for your position, and warns of interference when the two differ by more than 18%, clearing once they are back within 13%. That is a coarser test than the range on this page — at Casper, 18% is 9.4 µT against 4.5 µT — so it catches large interference, not small, and it does not run the dip check, so the sideways field described above can pass it.

Related: magnetic declination and true north, how far a stray field turns a compass, how a phone derives a heading from its sensors and checking a compass against the sun.

Sources