World Magnetic Model 2010

Calculate Earth's magnetic field at specific location and time using World Magnetic Model 2010 (WMM2010)




The WMM2010 block implements the mathematical representation of the National Geospatial Intelligence Agency (NGA) World Magnetic Model 2010. The WMM2010 block calculates the Earth's magnetic field vector, horizontal intensity, declination, inclination, and total intensity at a specified location and time. The reference frame is north-east-down (NED).


You cannot use this block to model the Earth magnetic field above an altitude of 1,000,000 meters.



Specifies the input and output units:

UnitsHeightMagnetic FieldHorizontal IntensityTotal Intensity
Metric (MKS)MetersNanoteslaNanoteslaNanotesla
Input decimal year

When selected, the decimal year is an input for the World Magnetic Model 2010 block. Otherwise, a date must be specified using the dialog parameters of Month, Day, and Year.


Specifies the month used to calculate decimal year.


Specifies the day used to calculate decimal year.


Specifies the year used to calculate decimal year.

Action for out-of-range input

Specify if out-of-range input invokes a warning, error or no action.

Output horizontal intensity

When selected, the horizontal intensity is output.

Output declination

When selected, the declination, the angle between true north and the magnetic field vector (positive eastwards), is output.

Output inclination

When selected, the inclination, the angle between the horizontal plane and the magnetic field vector (positive downwards), is output.

Output total intensity

When selected, the total intensity is output.

Inputs and Outputs

InputDimension TypeDescription



Contains the height, in selected units.



Contains the latitude in degrees.



Contains the longitude in degrees.

Fourth (Optional)


Contains the desired year in a decimal format to include any fraction of the year that has already passed. The value is the current year plus the number of days that have passed in this year divided by 365.

The following code illustrates how to calculate the decimal year, dyear, for March 21, 2010:

%%%END CODE%%%
OutputDimension TypeDescription


VectorContains the magnetic field in selected units.

Second (Optional)

 Contains the horizontal intensity in selected units.

Third (Optional)

 Contains the declination in degrees.

Fourth (Optional)

 Contains the inclination in degrees.

Fifth (Optional)

 Contains the total intensity in selected units.


The WMM2010 specification produces data that is reliable five years after the epoch of the model, which is January 1, 2015.

The internal calculation of decimal year does not take into account local time or leap seconds.

The WMM2010 specification describes only the long-wavelength spatial magnetic fluctuations due to the Earth's core. Intermediate and short-wavelength fluctuations, contributed from the crustal field (the mantle and crust), are not included. Also, the substantial fluctuations of the geomagnetic field, which occur constantly during magnetic storms and almost constantly in the disturbance field (auroral zones), are not included.


Introduced in R2010a