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International Geomagnetic Reference Field (IGRF) Model

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International Geomagnetic Reference Field (IGRF) Model


Drew Compston (view profile)


30 Dec 2011 (Updated )

Compute the Earth's magnetic field at points in space according to the IGRF model.

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The International Geomagnetic Reference Field (IGRF) is an internationally agreed upon mathematical model of the Earth's magnetic field. This program is a conversion of the FORTRAN subroutines that make the calculation into MATLAB. It does not use a compiled FORTRAN mex file, which probably makes it slower but at the advantage of being easier to use (as no compilation is necessary). In fact, my motivation in writing the program was to provide an IGRF implementation in MATLAB with minimal "fuss." Another motivation was a vectorized IGRF function, which this function is (with a separate routine adapted directly from the FORTRAN code that is faster for scalars implemented as well).
The following files are provided:
-igrf.m: Computes Earth's magnetic field at a point(s).
-igrfline.m: Gives the coordinates along a magnetic field line starting at a given point.
-getigrfcoefs.m: Extracts coefficients from the .dat files provided on the IGRF website and saves them to a .mat file.
-igrfcoefs.mat: IGRF coefficients of the 12th IGRF generation (most recent as of 2015).
-loadigrfcoefs.m: Loads the proper IGRF coefficients at a given time (making the necessary interpolation).
-*grf*.dat: 12th generation IGRF coefficient data files.
-plotbline: Plots a magnetic field line.
-plotbearth: Plots a number of magnetic field lines.
-geod2ecef: Converts geodetic coordinates to ECEF coordinates.
-ecef2geod: Converts ECEF coordinates to geodetic.
The only prerequisite to running either the function IGRF or the function IGRFLINE is to put the file igrfcoefs.mat in the MATLAB search path. The program is designed to be scalable with time: As new IGRF generations are released, simply replace the old .dat files with their newer versions in a subfolder called 'datfiles' within the same directory that the function getigrfcoefs.m is located and run getigrfcoefs, and then replace the file it generates (igrfcoefs.mat) with the old .mat file. Updates happen every five years, with the last update occurring in 2015. New .dat files will hopefully continue to be uploaded to the following ftp:
Finally, I have included two example scripts showing how the function IGRFLINE works: plotbline.m and plotbearth.m. These scripts both utilize the Mapping Toolbox to plot globes upon which magnetic field lines are plotted, but if the user does not have that package, a crude globe with just latitude and longitude lines is shown.

I've made some cursory comparisons with the online IGRF calculator at and found this function to be accurate to within 1 nT. I'm not sure why there is a discrepancy between the two, but my guess is round-off error.


Igrf Magnetic Field inspired this file.

Required Products MATLAB
MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (36)
16 Mar 2017 mary yang

Hi Drew,

Your work is excellent! I want to calculate the geodetic coordinate of the magnetic north pole .Could you tell me how can I do?

21 Feb 2017 Drew Compston

Drew Compston (view profile)

Sulav: If you're curious about the internals, I actually don't know why when inputting geodetic coordinates that the magnetic field is scaled like that in the last three lines. I got that bit of code from the original FORTRAN. I haven't check this myself, but you should get the same magnetic field at the same point in space regardless of whether the COORD input is 'geocentric' or 'geodetic'. Now that does NOT mean that these two statements will result in the same output:

>> igrf(now, 0, 0, 0, 'geoc')
>> igrf(now, 0, 0, 0, 'geod')

because (0, 0, 0) in geocentric coordinates is not the same point in space as (0, 0, 0) in geodetic coordinates. You'd actually have to convert between the two systems to determine what one point is in the other system. If you want to do this, you might reference, for example,

The program itself makes the computation of Earth's magnetic field in spherical coordinates. That is, when you provide a LATITUDE, LONGITUDE, and ALTITUDE where you want the magnetic field vector components, the program figures out where those are in a spherical coordinate system with an origin at Earth's center. Again, this is only relevant if you're interested in the internals.

Finally, I'll just say in case it is your cause for confusion: The output is a vector field, so it doesn't really make sense to convert it to ECEF, as that coordinate system defines a point in space, not a vector field. You could convert the coordinates of that point in space from geodetic latitude, longitude, and altitude that you input to ECEF using the provided function, but that wouldn't change the output magnetic vector field there.

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21 Feb 2017 Sulav

Sulav (view profile)

Thanks a lot for this great work.

But, I am getting confused with all these reference frames.So, to obtain the output in geodetic coordinates we have to use the last three lines, is it?

And what to do, to convert the values to ECEF co-ordinates? Will the given geod2ecef work? To me, it seems like it works only for latitude, longitude values.

06 Jan 2017 Minjie Fan

19 Nov 2016 Alison Moraes

Is there a way to get the geomagnetic longitude using your igrf function?

16 Nov 2016 M J Schwartz

Sorry, I wasn't thinking... igrf.m is in Matlab code, so it is trival to look for myself. The answer to my question is that the output is in the same coordinate frame as the input, selected by COORD to be ['geodetic'] or 'geocentric'.

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12 Nov 2016 Drew Compston

Drew Compston (view profile)

The output is the vector components of the magnetic field at each position given by the inputs. The output components specifically are those directed northward, eastward, and downward, respectively for Bx, By, and Bz. These are equivalent to the spherical coordinate components elevation (or -inclination), azimuth, and -radial. The requested input coordinate positions are interpreted as either geodetic or geocentric depending on the coord input, which in either case are converted to the ECEF frame.

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02 Nov 2016 CyberJo

great work. I am just wondering what is the reference frame of the output? Bx, By and Bz are in North, East and Down. Does that means the output is on NED frame?

14 Jul 2016 nikhil raykar

11 Mar 2016 Peter Gorham

05 Mar 2016 Yaguang Yang

Thank you very much! I wrote some quick and dirty code yesterday for my application. Your info is very helpful.

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05 Mar 2016 Drew Compston

Drew Compston (view profile)

I wrote some codes to do more or less what you're asking I think for a class, but because it was for a class it isn't really at a level worth posting on here. I think there are a lot of orbital mechanics toolboxes available you could use. A quick search on the exchange yields an Orbital Mechanics Library (File ID: #13439) that probably is similar to my codes (also done for a class) but likely more organized. Take a look at that and see if it will work for you.

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29 Feb 2016 Yaguang Yang

Hi Drew,

Very nice work! I have an application that prevents me from directly using your code. I would like to see if you have a solution for my problem. Assuming a spacecraft orbit is circular, given the ascending node (assuming "now" the spacecraft pass the node), spacecraft altitude, and inclination, one should be able to calculate the coordinate of the spacecraft at any time after time "now" then use the coordinate and your code to find the magnetic field vector at the position of the spacecraft for any time after the time "now". Do you have a code or the formulas to compute the spacecraft coordinate given ascending node, altitude, and inclination so that one can use your code?

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24 Feb 2016 Drew Compston

Drew Compston (view profile)

Note in general when having a question about a program, it always helps to say exactly what you input. For example:
>> igrf(now, 0, 0, 0)
ans =
27546 -2545.8 -15893
So yes, the units are definitely nT. As a guess, I wondered if you were inputting a radius in m. Apparently you are, as:
>> igrf(now, 0, 0, 6371e3)
ans =
2.934e-05 -4.7516e-06 2.9438e-06
But if you read the description, note that the fourth input is height from the Earth's surface in km when coord is 'geodetic' (the default). In geocentric, the fourth input is radius from the center of the Earth, but in km. So:
>> igrf(now, 0, 0, 6371, 'geoc')
ans =
27647 -2551.9 -15986

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24 Feb 2016 pedro nuñez

Im not sure if the units given by the function igrf for the magnetic field are in Teslas or in nanoteslas, because the description says that is in nanoteslas but then the result given I think is too small to be in nanoteslas (something to the order of 10^-5). Could you help me with that?

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11 Feb 2016 Drew Compston

Drew Compston (view profile)

I'm not sure why there was no igrf1925.dat. It looks like the program probably broke if you asked for a value between 1925 and 1930. I've uploaded a new version that should be more robust in that case (not assuming 5 year gaps between IGRF coefficient values) and included the igrf1925 coefficients.

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10 Feb 2016 Ryan Lewis

I am using this code for part of my final year dissertation project. I was wondering why there is no igrf1925.dat file? I have found the data and made my own .dat file however the code doesn't seem to recognize it. Any help would be much appreciated. Apart from that, working great and it's saved a lot of work for me so thanks!

13 Jan 2016 Huy Hoang

Highly appreciate your nice work.

08 Oct 2015 Pat Welch

Meltem Akan, please email me, pat at, for an updated version of Drew's code which reads in the IGRF12 Excel file.

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10 Apr 2015 meltem akan

Pat Welch hello. I am working on the same project. I don't know how to contact with you , but I will be happy if we can work together.

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20 Mar 2015 Pat Welch

Do you have an update to use the IGRF12 database for 2015-2020 yet? If not I'll take care of it, but please let me know.

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02 Dec 2014 John

John (view profile)

Works pretty well so far.

09 Oct 2014 Drew Compston

Drew Compston (view profile)

You should be able to get IGRF values at the website listed in the description above:

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06 Oct 2014 XAXRXTX

thanks for your response, in my case I used the formulas figured in wertz text book and they are the same as those figured in the paper that you indicated, and also I got the same results as yours.

now, if it's possible, could you show me how can I compare this model with the online model ?

thanks for your help and your time

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06 Oct 2014 Drew Compston

Drew Compston (view profile)

I got the formulas for P(n,m) and dP(n,m) by looking at the direct Fortran translation of the IGRF done by Charles Rino (#28874, listed as inspiration for this file) and figuring out what that program was doing. The formulas in the paper here ( are different, and I am not sure why.

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04 Oct 2014 XAXRXTX

Hi Drew

I have a question about Pn,m and dPn,m ,
where you get this formula to calculate them.

thanks in advance

25 Apr 2014 Cesar Alberto Vazquez Garcia

Good work

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03 Apr 2014 Drew Compston

Drew Compston (view profile)

I do have an IRI and MSIS code that works by querying an online interface. So it's a lot slower than this but gets the job done. I don't foresee converting the FORTRAN source code for models like the IRI or Tsyganenko any time soon (if ever). The IGRF model is much simpler than those as it is really just one (vector) equation.

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03 Apr 2014 XAXRXTX

this is a very helpfull work for me,
do you have another mathematical model describing the atmospheric perturbations like MSIS or Jacchia models

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12 Mar 2014 cao

cao (view profile)

09 Aug 2013 Paul

Paul (view profile)

Great work. Any plans do something similar with the Tsyganenko models?

06 Jul 2012 Anna Kelbert

It's amazing how fast this thing is! Takes me much longer to compute the fields on a grid with a homemade spherical harmonic toolbox.

13 May 2012 Charles Rino

Charles Rino (view profile)

A significant improvement over my own direct translation of igrf11syn.
Easier to use, with cleaner interface with spherical harmonic coefficient files. Field tracing utilities are also very useful.

Users may find GPS transformation helpful:

25 Jan 2012 Michael

I have noticed that results are inconsistant depending on the size if the inputs:

atand(Bz./sqrt(Bx.^2 + By.^2))

Gives an inclination of -48.9117, while:

atand(Bz./sqrt(Bx.^2 + By.^2))

Gives an inclination of -48.6375, and other sized vectors produce slightly different results.

Otherwise it is well done.

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25 Jan 2012 Michael

31 Dec 2011 christie harper

nice job. few minor issues.

isleapyr function not included
here is a simple one
function [is_leap] = leap_year(year_in)
is_leap = (~mod(year_in,4) && mod(year_in,100)) || ~mod(year_in,400);

and the
referenced version of ecef2lla does not return a matrix but vectors
change function signature to
function [lla] = ecef2lla(ecx)
change returns to
lla = zeros(length(glat),3);
lla(:,1) = glat;
lla(:,2) = glon;
lla(:,3) = eht;

also your spin logic is broken at the end
change while true to while spin

01 Jan 2012 1.3

Fixed the issues detailed in Christie Harper's comment (including some additional ones relating to the differences between MATLAB's built-in ecef2lla and the free file exchange ecef2lla) and made some minor changes to speed up the functions slightly.

25 Jan 2012 1.4

Fixed bug described in Michael's comment. For those interested, it resulted from mistakenly calculating dP using only the last latitude input rather than the vector.

25 Apr 2012 1.5

Provided my own ECEF to geodetic conversion routine.

07 Aug 2012 1.6

Added capability to plot globe without mapping toolbox and minor bug fix.

02 Nov 2012 1.7

Adjusted initial comment block in IGRF with correct definition of inclination using atan2 (rather than atan).

16 Oct 2014 1.8

Apparently, the earlier bug pointed out by Michael on 25 Jan 2012 resurfaced. Presumably the fix I had implemented before got undone, so this update includes that fix again.

29 Oct 2014 1.9

Removed 'years' variable from loadigrfcoefs.mat.

20 Mar 2015 1.10

Includes 2015 coefficients (12th generation IGRF).

20 Mar 2015 1.11


20 Apr 2015 1.12

Updated description text to reflect my most recent update: The newest 2015 coefficients are now included.

11 Feb 2016 1.13

Added igrf1925 coefficients and made loadigrfcoefs.m more robust to different than 5 year gaps between coefficient files.

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