Daily Magnetic Variation Calculator

This calculator works out the daily magnetic variation (also called magnetic declination) for a given date and location, returning the angle between true north and magnetic north in degrees and minutes. You enter the date, latitude, and longitude, and the calculator uses the standard IGRF (International Geomagnetic Reference Field) model coefficients to compute the declination, plus the annual change rate. The result is the magnetic variation you would apply to a compass bearing to get a true bearing, or vice versa.

Formula

The daily magnetic variation is the angle between true north (geographic pole) and magnetic north (the direction a compass needle points) at a specific location and time. The standard model used is the International Geomagnetic Reference Field (IGRF), which is updated every five years by the International Association of Geomagnetism and Aeronomy (IAGA). The declination D is computed from the model’s spherical harmonic coefficients:

D = atan2(Y, X)

where X and Y are the north and east components of the magnetic field vector at the location, derived from the IGRF coefficients. The annual change (in degrees per year) is the secular variation, also from the model.

• Latitude – geographic latitude in degrees, positive north, negative south.
• Longitude – geographic longitude in degrees, positive east, negative west.
• Date – the date for which the variation is calculated; the model accounts for secular change.

Worked Example

Using the default values: Date = 2025-06-15, Latitude = 40.7128°N (New York City), Longitude = -74.0060°W.

1. Convert the date to decimal years: 2025.45 (approximately).
2. Look up the IGRF coefficients for epoch 2025.0 and apply the secular variation to get the field at 2025.45.
3. Compute the north (X) and east (Y) components of the magnetic field at the location.
4. Calculate declination: D = atan2(Y, X).

For New York on that date, the IGRF gives a declination of about -12.5° (west) and an annual change of about +0.1° per year (moving eastward). The calculator shows -12.50°.

Why Magnetic Variation Changes Daily

Magnetic declination is not constant; it changes slowly over years due to changes in Earth’s molten outer core, and it also has a small daily variation (diurnal) caused by solar wind and ionospheric currents. The daily variation is typically less than 1 degree and is usually ignored for navigation, but it can be significant for precise surveying or when using a compass near the magnetic poles. The IGRF model provides the average annual value, not the daily fluctuation.

How to Use the Calculator

Enter the date, latitude, and longitude of your location. The calculator returns the magnetic declination in degrees (positive east, negative west) and the annual change. To convert a magnetic bearing to a true bearing, add the declination if east, subtract if west. For example, if your compass reads 90° (due east) and the declination is -12.5°, the true bearing is 90° – (-12.5°) = 102.5°.

Common Mistakes and Misconceptions

• Mixing east/west sign – Many people forget that west declination is negative. Always check: if you are west of the agonic line (where declination is zero), your compass points east of true north, so the declination is negative.
• Using the wrong date – The IGRF changes over time; using an old value can give errors of several degrees in some regions.
• Confusing magnetic variation with magnetic dip – Variation is horizontal angle; dip is vertical angle (inclination).
• Assuming declination is constant – Even within a day, it can change slightly; for high accuracy, use a real-time service.

Limits of the IGRF Model

The IGRF is a mathematical model that approximates Earth’s magnetic field. It is accurate to about 0.5° in declination for most of the world, but near the magnetic poles the field is highly variable and the model may be less accurate. Also, the model does not include the daily solar-driven variation, which can be up to a few degrees at high latitudes. For navigation, the annual change is usually applied to correct maps, but for precision work, use a current magnetic survey or a real-time magnetic field calculator.

Alternatives and Related Tools

If you need the daily variation for a specific date and time, you can use the World Magnetic Model (WMM) which is similar to IGRF and used in many GPS devices. For real-time values, you can use online services like the NOAA Magnetic Field Calculator. For compass correction, you can also use a sun or star azimuth to determine declination empirically.

Frequently Asked Questions

What is the difference between magnetic variation and declination?

They are the same thing. Magnetic variation is the term used in aviation and marine navigation; declination is the term used in land surveying and geology. Both refer to the angle between true north and magnetic north.

Why does the calculator ask for a date?

Because the magnetic field changes over time. The IGRF model includes secular variation, so the declination for a given location changes by a few tenths of a degree per year. Entering the date ensures you get the current value.

Can I use this for compass navigation on a hike?

Yes, but remember that the daily variation is usually small (less than 1°). For most hiking, a declination value accurate to the nearest degree is sufficient. The calculator gives that, but you should also account for local magnetic anomalies if you are near iron deposits.

How do I convert a bearing using the declination?

If your declination is east (positive), add it to your magnetic bearing to get true bearing. If west (negative), subtract it. For example, if your compass reads 270° and declination is +5°, your true bearing is 275°. If declination is -5°, your true bearing is 265°.

Why is the declination different from my GPS reading?

GPS receivers typically use the WMM model, which is similar but not identical to IGRF. Also, your GPS may be set to display true north or magnetic north. Check your device settings to see which one it shows.

Is the daily variation significant for aviation?

For aviation, the daily variation is usually ignored because it is small compared to other errors. However, pilots do apply the annual change to update charts. The IGRF value is sufficient for flight planning.

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in date | Date | - | 2025-06-15 | 0
in lat | Latitude | deg | 40.7128 | -90
in lon | Longitude | deg | -74.0060 | -180
out decl | Magnetic declination | deg | (declination from IGRF) | 2
out annual | Annual change | deg/yr | (annual change from IGRF) | 2