Mag Variation Calculator: Find True Bearing

This calculator converts a magnetic bearing to a true bearing (or vice versa) using the local magnetic declination (variation) you enter. You input the bearing you have, the declination value, and the direction of declination (east or west), and the tool returns the corrected bearing in degrees. It also shows the intermediate steps so you can verify the math.

Formula

The core formula is simple addition or subtraction of the declination angle:

True Bearing = Magnetic Bearing + (Declination × Direction Factor)

Where:

• True Bearing (degrees) – the angle measured relative to geographic (true) north.
• Magnetic Bearing (degrees) – the angle measured relative to magnetic north (what a compass shows).
• Declination (degrees) – the angle between true north and magnetic north at your location. It changes over time and by location.
• Direction Factor – +1 for east declination, -1 for west declination. East declination means magnetic north is east of true north.

If you are converting from true to magnetic, simply reverse the sign: Magnetic = True − (Declination × Direction Factor).

Worked Example

Using the default values from the calculator:

• Bearing to convert: 90° (due east)
• Declination: 10° east
• Direction factor: +1 (east)

Calculation: 90 + (10 × 1) = 100° true bearing.

If you had a true bearing of 100° and wanted the magnetic bearing: 100 − 10 = 90° magnetic. The calculator’s second output shows this reverse conversion.

What Is Magnetic Variation?

Magnetic variation (also called magnetic declination) is the angle between the direction a compass needle points (magnetic north) and the direction of the geographic North Pole (true north). This angle is not constant; it varies depending on where you are on Earth and changes slowly over the years as the Earth’s magnetic field shifts. For example, in 2024, the declination in Seattle, Washington, is about 15° east, while in New York it is about 12° west. Knowing the local declination is essential for accurate navigation with a map and compass.

How to Use the Calculator

Follow these steps to get a correct result:

1. Determine whether your input bearing is magnetic (from a compass) or true (from a map).
2. Find the local declination for your area and the current year. You can get this from a topographic map (printed in the margin) or an online geomagnetic model.
3. Enter the bearing value in degrees (0–360).
4. Enter the declination magnitude (always a positive number) and select east or west.
5. Read the true bearing from the first output if you converted from magnetic, or the magnetic bearing from the second output if you converted from true.

Remember: the calculator assumes your input is the bearing you have. If you have a magnetic bearing, the first output is true; if you have a true bearing, use the second output to get magnetic.

Common Mistakes and Pitfalls

Several errors can lead to wrong bearings:

• Wrong direction sign: East declination is added when converting magnetic to true, but subtracted when converting true to magnetic. Mixing these up is the most common error.
• Using outdated declination: Declination changes by a few arc-minutes per year on average. A 20-year-old map may be off by several degrees.
• Forgetting to normalize the result: If your calculation gives a bearing outside 0–360°, add or subtract 360° to bring it into range. For example, 360° + 5° = 5° (not 365°).
• Confusing declination with deviation: Deviation is the error caused by magnetic interference on a specific compass, not the Earth’s field. This calculator does not account for deviation.

Limitations of the Formula

The simple addition formula works for most navigation purposes, but it ignores a few subtle effects:

• Grid convergence: On a map with a grid (like UTM), the grid north differs slightly from true north. This calculator uses true north, not grid north.
• Local magnetic anomalies: Iron deposits or man-made structures can cause local deviations that the global declination model does not capture.
• Compass accuracy: A typical handheld compass has an accuracy of ±2° to ±5°, so the calculated bearing is only as good as the compass.
• Time-dependent declination: The declination value changes annually; you must use the current value for your location and year.

Alternatives and Related Tools

If you need a more precise conversion, consider these options:

• Online geomagnetic calculators: These use global models (like WMM) to compute declination for any lat/lon and date. They are more accurate than a static map value.
• GPS devices: Most GPS receivers can display bearings in true or magnetic mode, automatically applying the current declination.
• Navigation apps: Many apps for hiking or sailing include a declination setting that adjusts compass readings automatically.
• Map and compass courses: If you are new to navigation, a practical course will help you understand when to apply declination and how to avoid errors.

Frequently Asked Questions

What is the difference between magnetic variation and declination?

They are the same thing. The term “variation” is often used in aviation and marine navigation, while “declination” is common in land navigation and geology. Both refer to the angle between true north and magnetic north.

Why does declination change over time?

The Earth’s magnetic field is generated by moving molten iron in the outer core, which is not static. This causes the magnetic poles to drift and the field to change shape, so the angle between true and magnetic north at any location shifts gradually over years.

How do I find the declination for my location?

Topographic maps usually print the declination in the margin, along with the annual change. For a current value, use an online geomagnetic model (such as the World Magnetic Model) by entering your latitude and longitude. Many GPS units also display the current declination.

Can I use this calculator for aviation or marine navigation?

Yes, the math is the same, but for aviation and marine you must also account for wind or current drift when planning a course. This calculator only converts between magnetic and true bearings; it does not compute groundspeed or drift correction.

What if my bearing is negative or greater than 360?

Bearings are conventionally expressed as 0–360°. If your calculation yields a negative value, add 360°; if it exceeds 360°, subtract 360°. For example, −10° becomes 350°, and 370° becomes 10°.

Is the calculator accurate enough for hiking?

Yes, for most outdoor navigation it is accurate to the degree you enter the declination. Since a typical compass has an accuracy of a few degrees, this calculator’s precision is more than sufficient for hiking, orienteering, and general map reading.

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in b | Bearing to convert | deg | 90 | 0
in d | Magnetic declination | deg | 10 | 0
sel dir | Declination direction | East=1, West=-1
out true | True bearing | deg | b + (dir * d) | 2
out mag | Magnetic bearing (if converting true to mag) | deg | b - (dir * d) | 2