Declination is the angle between magnetic north (where your compass points) and true north (the geographic North Pole). To calculate it for your location, you need your latitude, longitude, and the current date, which you plug into a free online calculator maintained by NOAA. For solar declination, used in solar energy and astronomy, you apply a trigonometric formula based on the day of the year. Here’s how both types work and how to use them in practice.
Magnetic Declination vs. Solar Declination
These are two entirely different measurements that share a name. Magnetic declination matters for navigation: it tells you how far off your compass reading is from true north. Solar declination matters for solar panel placement and understanding seasonal sunlight: it describes how far the sun sits above or below the equator on a given day. Most people searching “how to calculate declination” need one or the other, so this article covers both.
How Magnetic Declination Works
Your compass needle aligns with Earth’s magnetic field, which doesn’t point to the geographic North Pole. The angle between where your compass points (magnetic north) and true north is your magnetic declination. When magnetic north falls east of true north, declination is positive. When it falls west, declination is negative.
This offset varies dramatically depending on where you stand on the planet. In parts of the eastern United States, declination might be 10 to 15 degrees west. In Alaska, it can exceed 20 degrees. Along a narrow band called the agonic line, declination is zero and your compass points directly to true north. The value also shifts over time because Earth’s magnetic field is constantly changing, a phenomenon called secular variation. A declination value from 10 years ago for the same spot could be off by several degrees today.
Using NOAA’s Free Calculator
You don’t need to do the math yourself for magnetic declination. NOAA’s National Centers for Environmental Information provides a free online magnetic field calculator that does the heavy lifting. You enter three inputs:
- Latitude and longitude of your location, in either decimal degrees or degrees/minutes/seconds
- Date in year, month, and day (the form defaults to today’s date)
The calculator returns your declination value along with other magnetic field components. If you only need the declination for a single day between 1900 and the present, NOAA also offers a simplified declination-only calculator. Both tools are free and require no account.
Behind the scenes, these calculators rely on the World Magnetic Model (WMM), a mathematical representation of Earth’s magnetic field jointly maintained by NOAA and the British Geological Survey. The current version, WMM2025, was released on December 17, 2024, and is valid through late 2029. A more detailed scientific model called the International Geomagnetic Reference Field (IGRF) is now in its 14th generation, finalized in November 2024, and represents the magnetic field using a series of mathematical coefficients out to degree 13. For practical navigation, the WMM calculator gives you everything you need.
Reading Declination on a Topographic Map
Every USGS topographic map includes a declination diagram at the bottom margin. It shows three reference directions: true north (marked with a star), magnetic north (labeled “MN”), and grid north (labeled “GN”). The angle between the star and MN is the magnetic declination for that map’s location, printed in degrees alongside the diagram.
One important caution: the declination printed on the map was accurate when the map was published. If the map is decades old, the actual declination at that location may have shifted. Check NOAA’s calculator for a current value before relying on the map’s printed number.
Converting Between Magnetic and True Bearings
Once you know your declination, converting between what your compass reads and the true bearing is straightforward arithmetic. The core formula is:
True bearing = Magnetic bearing + Declination
Because east declination is positive and west declination is negative, the signs handle the direction for you. If your declination is +12° (east), and your compass reads 150°, your true bearing is 162°. If your declination is -8° (west) and your compass reads 150°, your true bearing is 142°.
A common memory aid: “East is least, west is best.” When declination is east, you subtract it from the true bearing to get the magnetic bearing (the number gets “least”). When declination is west, you add it to the true bearing to get the magnetic bearing (the number gets the “best,” or bigger value). This mnemonic works specifically when converting from true to magnetic. When going from magnetic to true, you reverse it: add east declination, subtract west.
Many modern compasses let you set a declination adjustment on the bezel so every reading is automatically corrected. If your compass supports this, dial in your local declination and you can read true bearings directly without doing any mental math in the field.
Calculating Solar Declination
Solar declination describes how many degrees north or south of the equator the sun appears at solar noon. It swings from about +23.45° at the summer solstice (sun directly over the Tropic of Cancer) to -23.45° at the winter solstice (sun over the Tropic of Capricorn), and crosses 0° at each equinox.
The standard formula, often called Cooper’s equation, is:
δ = 23.45° × sin(360/365 × (d + 284))
Here, δ (delta) is the solar declination in degrees, and d is the day number of the year (January 1 = 1, February 1 = 32, and so on). The number 284 is a correction factor that aligns the formula with the vernal equinox falling around March 21-22. Some versions of the formula write this as (d – 81) instead of (d + 284), which is mathematically equivalent since 284 + 81 = 365.
To work through an example: on the summer solstice, roughly June 21, d = 172. Plugging in: 360/365 × (172 + 284) = 360/365 × 456 = 449.6°. The sine of 449.6° (which wraps around to sin(89.6°)) is approximately 1.0, giving δ ≈ 23.45°. That checks out, since the solstice is when declination peaks.
For a spring date like April 15 (d = 105): 360/365 × (105 + 284) = 383.7°. Sin(383.7°) = sin(23.7°) ≈ 0.402, so δ ≈ 23.45 × 0.402 ≈ 9.4° north. This is useful for calculating optimal tilt angles for solar panels or predicting sunrise and sunset positions at your latitude.
Why Declination Values Change Over Time
Earth’s magnetic field is generated by the motion of molten iron in the outer core, and those currents shift continuously. This means your local magnetic declination drifts year after year. In some regions the change is small, a fraction of a degree per year. In others, particularly at high latitudes, it can be more noticeable. This is why the World Magnetic Model gets updated on a five-year cycle, with WMM2025 now superseding the previous WMM2020 version.
Solar declination, by contrast, follows the same predictable cycle every year driven by Earth’s 23.45° axial tilt. The formula above works for any year without adjustment, though very precise astronomical calculations account for leap years and slight orbital variations.
For magnetic declination, always use a current value. For solar declination, the formula is reliable as-is for any practical purpose including solar panel installation, garden planning, or amateur astronomy.