Magnetic North vs True North

This article is operational: how to actually convert bearings between magnetic, true, and grid north. The /learn/magnetic-declination-explained pillar covers what declination is and how it varies in space and time; this companion focuses on what you do with that knowledge in the field.

The three norths

A bearing — a horizontal direction in degrees — has three common references:

True north

The direction along the local meridian toward the geographic North Pole. The bearing coordinate-system geometry uses. Defined unambiguously everywhere except at the geographic poles themselves.

True bearings are what GPS reports natively (the GPS receiver computes position in a true-Earth-relative frame and derives bearings from there). True bearings are what appear in coordinate calculations from lat/lon.

Magnetic north

The direction the horizontal component of Earth's magnetic field points. A freely suspended compass needle aligns with this direction. Differs from true north by the local magnetic declination (see /learn/magnetic-declination-explained).

Grid north

The direction along the y-axis of the map's projection grid — UTM, British National Grid, Lambert-93, State Plane, or any other planar grid. Differs from true north by the meridian convergence of the projection at the location.

For UTM (see /learn/utm-coordinate-system): the y-axis is northing, parallel to the central meridian of the UTM zone. At the central meridian, grid north exactly equals true north. Moving east or west from the central meridian, the meridians curve while the grid lines stay straight — so grid north and true north diverge by the meridian convergence angle.

Approximate convergence:

convergence ≈ (λ - λ_0) sin(φ)

Where λ is the longitude, λ_0 is the central meridian of the zone, and φ is the latitude. At the eastern or western edge of a UTM zone (∆λ = 3°), at latitude 60°, convergence is about 3° × sin(60°) ≈ 2.6°. Higher latitudes have larger convergence; near the equator it's minimal.

The declination diagram

Every USGS topographic map, every UK Ordnance Survey Explorer/Landranger map, and most military topographic maps include a declination diagram in the margin.

The diagram shows three arrows from a common point:

• Star symbol or asterisk — true north (geographic North Pole)
• GN or “grid” — grid north (the y-axis of the map's grid)
• MN or “magnetic” — magnetic north (compass-needle direction)

Between the arrows are labeled angles:

• Declination: angle between true north and magnetic north, with east or west designation.
• Convergence: angle between true north and grid north, with east or west designation.

The diagram is dated — typically with the year of map publication or the year of declination measurement. As declination drifts (~0.1° per year typical), the printed value becomes inaccurate. A 20-year-old map's declination value may be 2° off; a 50-year-old map could be 5° off.

Always check current declination for serious navigation: use the NOAA NCEI WMM calculator (https://www.ngdc.noaa.gov/geomag/calculators/magcalc.shtml) or any modern smartphone compass app, which uses WMM internally.

USGS convention

USGS topographic maps print the declination diagram in the lower-left margin. Newer maps (post-2010) use the standard graphic; some older maps used variant styles. The diagram labels the year of declination measurement.

UK Ordnance Survey convention

OS Explorer (1:25,000) and Landranger (1:50,000) maps print the “Magnetic North” note in the lower margin. The note states the year of the declination value and the annual rate of change (so the user can extrapolate to current).

Military map convention

U.S. Army FM 3-25.26 specifies the declination diagram prominently. Military training emphasizes the G-M angle (grid-to-magnetic, the combined declination and convergence correction) as the operational quantity for compass-to-map use.

The conversion arithmetic

The two key relationships:

true = magnetic + declination
true = grid     + convergence

Where declination and convergence are positive for east, negative for west (the magnetic or grid reference direction is east of true).

Magnetic ↔ true

true_bearing = magnetic_bearing + declination
magnetic_bearing = true_bearing - declination

Mnemonic: “east is least, west is best.”

• East declination is positive, so magnetic + positive = true. Therefore magnetic < true (magnetic is “least”).
• West declination is negative, so magnetic + negative = true. Therefore magnetic > true (magnetic is “best”, meaning highest numerical value).

Worked examples:

| Magnetic bearing | Declination | True bearing | Notes | | ---------------- | ----------- | ------------ | ----- | | 087° | +12° (E) | 099° | east | | 087° | -15° (W) | 072° | west | | 270° | +5° (E) | 275° | east | | 270° | -5° (W) | 265° | west | | 358° | +5° (E) | 003° | wraps | | 003° | -5° (W) | 358° | wraps |

The wraps are important: bearings are modulo 360°. A result of 365° should be normalized to 5°; a result of -3° should be normalized to 357°.

True ↔ grid

true_bearing = grid_bearing + convergence
grid_bearing = true_bearing - convergence

The same sign convention. Magnitude is usually smaller than declination (convergence rarely exceeds 3° for UTM or BNG at mid-latitudes).

Magnetic ↔ grid

Two ways to compute, both equivalent:

grid = magnetic + (declination - convergence)
magnetic = grid + (convergence - declination)

Or the cleaner two-step approach: magnetic ↔ true via declination, then true ↔ grid via convergence.

The combined quantity (declination − convergence) is the G-M angle in U.S. Army terminology. Some maps print the G-M angle directly to simplify field calculation.

Worked operational example

You're hiking near Mount Hood, Oregon. You consult a USGS topographic map dated 2018. The declination diagram shows:

• True north: vertical (reference)
• Magnetic north: 15° east of true
• Grid north (UTM zone 10): 1° west of true (you're east of the zone's central meridian)
• Year: 2018

You want to walk from your current position to a peak. Plotting on the map (which has grid lines), you measure the grid bearing as 075°.

To set your compass:

1. Convergence correction: convergence is west at this location (grid north 1° west of true) — so convergence is -1°.

   true_bearing = grid_bearing + convergence
                 = 075° + (-1°)
                 = 074°
   

2. Declination correction: declination is +15° E as printed, but it's 2018 data. Annual change at this location is roughly -0.1°/year, so 2026 value is about +14° E.

   magnetic_bearing = true_bearing - declination
                    = 074° - 14°
                    = 060°
   

3. Set compass to 060°, walk in that direction.

If you skipped both corrections and walked the bearing 075° magnetic from the map (treating grid = true = magnetic — a common beginner error), you'd be off by ~15° (the declination dominates) and arrive about 1 km off-target for every 4 km traveled.

Marine charts

Marine charts have their own convention. NOAA nautical charts and UK Admiralty charts print compass roses: double-circle graphics with the outer ring in true bearings and the inner ring in magnetic bearings (at the chart's date). Both are labeled in degrees with cardinal points (N, NE, E, SE, S, SW, W, NW).

The declination at the rose is printed in the centre, along with the date and annual rate of change. Multiple roses are distributed across the chart at convenient locations so the user can read the local declination without computation.

Marine practice is to plot all bearings in true on the chart and convert to/from magnetic only when reading the compass. The chart-to-real-world conversion is:

1. Plot the route in true bearings.
2. Convert each leg to magnetic (subtract declination).
3. Apply the ship's deviation for that heading (a per-ship correction for local magnetic interference).
4. Steer the resulting compass course.

The deviation table (a ship-specific document) and the declination from the chart combine to produce the compass course.

Hiking compasses

Modern hiking compasses commonly have an adjustable declination bezel — a screw or wheel that lets the user set the declination correction once, after which all bearings read directly in true. Quality models (Suunto MC-2, Brunton TruArc, Silva Ranger, etc.) have this feature.

The adjustment:

• Determine the local declination (from the map's declination diagram or a current WMM lookup).
• Use the small screwdriver provided with the compass to rotate the orienting arrow by the declination amount, in the appropriate direction.
• After adjustment, the compass reads true bearings directly.

This eliminates the per-bearing conversion arithmetic. It's good practice for hikers in unfamiliar terrain; declination errors are a common source of off-trail disasters.

Smartphone APIs

Modern smartphones expose both magnetic and true bearings:

iOS: CLHeading object from Core Location:

• magneticHeading — uncorrected magnetometer reading
• trueHeading — WMM-corrected (or -1 if location is unknown)
• headingAccuracy — uncertainty in degrees

Android: SensorManager + GeomagneticField:

• Sensor.TYPE_MAGNETIC_FIELD — raw magnetometer
• GeomagneticField class — apply WMM-based declination
• getDeclination() returns the local correction in degrees

Apps that show a compass to the user typically use true heading by default — the user sees a needle pointing at true north regardless of local declination. Apps for hikers or pilots may show both or let the user choose.

Common errors

Forgetting to update declination. A topographic map from 2000 has declination data that's now 25 years old; at typical 0.1°/year drift, that's 2.5° inaccuracy — enough to be off by 50 meters per 1 km travelled. Always update from a current WMM source.

Sign errors. Positive east, negative west. Many people get this backward and end up with a sign-flipped correction that doubles the error. The mnemonic “east is least, west is best” helps as a sanity check.

Direction of conversion. magnetic → true adds declination (when declination is positive). true → magnetic subtracts. Reversing these doubles the error.

Confusing grid and true. On a UTM map, grid north deviates from true north by the meridian convergence. For low-precision uses this is often ignored, but for surveying or piloting it matters.

Confusing magnetic north (the local field direction) with the Magnetic North Pole (a specific point in the Arctic). A compass aligned with the local field points along the field lines, not directly at the Magnetic Pole. The two coincide only for an observer exactly on the local agonic line and exactly at the same longitude as the Pole — rare.

Treating declination as constant. It drifts with time, varies with location, and can shift by several degrees over a few hundred kilometres. Always use the local current value.

Common misconceptions

“The compass always points to magnetic north.” It points along the local horizontal magnetic field direction. Near the magnetic pole, the field is nearly vertical, the horizontal component is small, and the compass is unreliable. Compass operation breaks down within ~1,000 km of the magnetic pole.

“A GPS receiver doesn't need to know declination.” GPS computes position from satellite ranges, which is true-Earth-relative. Declination doesn't affect GPS positioning. But a GPS receiver that displays a compass-style bearing needs to either (a) use its motion vector for true heading (works only when moving), or (b) include a magnetometer and apply WMM (most smartphones do this).

“True north is the same direction everywhere.” True north is the direction along your local meridian. Meridians converge at the poles, so two people 1,000 km apart and on different meridians have different absolute “true north” vectors — though both point to the geographic North Pole. For short distances, the difference is negligible; for intercontinental distances, see /learn/great-circle-distance.

“Grid north exists only on UTM maps.” Any projection with a planar grid (UTM, BNG, Lambert, State Plane, Web Mercator) defines its own grid north. The convergence relationship to true north is specific to the projection.

“Declination is a single number for a country.” It varies continuously across the country's area. The continental US ranges over 40° of declination (+17° in Maine to -23° in Washington). A national-average value is meaningless for any specific location.

“The G-M angle is the same as declination.” The G-M angle is the combined declination plus convergence — what the U.S. military uses for direct compass-to-grid bearing conversion. It includes both the geographic drift (declination) and the projection's grid orientation (convergence).

“Marine charts are always in true.” Marine charts print both true and magnetic references via the compass rose. Marine practice typically plots in true and converts to magnetic at the steering compass — but the chart itself supports both.

“A compass without an adjustable bezel is useless.” Fixed-bezel compasses are fine — they just require per-bearing arithmetic to convert. The adjustable bezel is a convenience, not a necessity.