Why doesn't a compass point to map north?
― In the mountains, you drift sideways about 100m for every 1km you walk
Before setting off, hikers and surveyors spread out their map and pencil in several slanted lines. These are called "magnetic north lines." The north a compass needle points to and the north on a map aren't the same north. In Japan, the gap between them is said to be roughly 5–10 degrees. A small angle — but it widens the further you walk.
You're walking through a forest with a map and compass. On the map, the hut you're heading for lies almost due north.
So you line up the compass needle and walk straight north. On the map, it's about a 1km walk.
But when you arrive, there's no hut. You've come out on a slope a little to the west instead. The compass isn't broken, and the map isn't wrong either.
There are only two reasons
Map north is the north that Earth's spin axis points to. Compass north is the north that Earth's own giant internal magnet points to. These two axes are misaligned from the start.
The magnetic field is generated inside the Earth, and its distribution is uneven from place to place. That's why the direction and size of the gap change depending on where you're standing.
Together, these two effects create the gap between "map north" and "needle north." This gap has a name: magnetic declination. In Japan, the needle always leans west — by about 9–10 degrees in Hokkaido, around 7.5 degrees in the Kanto region, and about 5 degrees in Okinawa.
Reason one: Earth's magnet sits at a tilt
The magnetic field around Earth is thought to be generated in the core at its centre. The magnetic axis this activity creates is tilted about a dozen or so degrees from Earth's spin axis. In other words, the needle isn't pointing at the map's North Pole itself.
What's more, needle-north doesn't sit still. It has kept drifting over long stretches of time — in the 20th century it sat north of Canada, but it's now said to have shifted toward Siberia. Map north never moves, but needle-north is a moving target. Look at the left side of Figure 1: you can see the vertical dotted line and the tilted solid line don't line up.
Reason two: the gap differs by location
If Earth were a neat bar magnet, the gap could be worked out with a single calculation. But the real magnetic field is unevenly distributed, varying in both strength and direction beneath continents and oceans.
Because of this, the gap has to be measured region by region. Japan's Geospatial Information Authority surveys geomagnetism nationwide and publishes maps showing how many degrees west the needle leans in each area. The bearing notes printed at the edge of topographic maps come from these surveys.
The gap also shifts from year to year. In Japan, the westward angle is said to be growing slightly, by a few minutes of arc a year (one minute being 1/60th of a degree). That's why using the notes on an old map without adjustment leaves you slightly off.
Airport runways are painted with numbers like "34" or "16." These are the bearing based on needle-north, divided by ten. When needle-north shifts, the number stops matching the runway's actual direction, so airports around the world have had to repaint their numbers over time. Using a moving landmark means even the writing on the ground eventually has to be rewritten.
Summary
A compass needle is honestly pointing at Earth's magnetic field. But because that field's axis doesn't line up with Earth's spin axis, it doesn't match map north. In Japan it leans roughly 5–10 degrees west, and that angle pushes you sideways more and more the further you walk. That's why, in the field, people draw a magnetic north line on the map before lining up the needle.
The needle isn't pointing at "north" —
it's simply pointing at the direction of Earth's magnet.
For how the needle itself comes to point north, see Why does a compass needle point north?, and for using a fixed landmark like a star, see Is Polaris the brightest star?
- Get a paper topographic map and find the note at the edge. It will say something like "western declination 7°10′," showing how many degrees west the needle leans.
- Using a protractor, draw several lines across the whole map, tilted left from the map's vertical lines by that angle. These are the magnetic north lines.
- Outdoors, place the compass on the map and rotate the whole map until the needle is parallel to the magnetic north lines. The map's orientation now matches the ground.
Near iron posts, cars, or power lines, the needle gets pulled off course. You can catch this by moving a few metres away and taking a second reading from a different spot.
Want to know more? ― Terms, formulas, and textbook linksWe label exactly which level each part belongs to, from middle-school science to university specialist courses
- MSCovered in middle-school science
- HSCovered in high-school "Basic Physics / Math I"
- HS+High-school advanced content, or textbook sidebar material
- Univ.Not taught in high school — university specialist content (geomagnetism)
- ResearchNot yet settled even at university level — an active research question
MSTerminology: this phenomenon has a name
- Magnetic declination: the angle between map north (true north) and the north a compass points to (magnetic north). In Japan, since the needle leans west, it's called "western declination."
- Magnetic north line: a line drawn on a map, tilted by the declination angle. It's a tool for aligning the needle with the map, used in the field for hiking and surveying.
- Magnetic dip (inclination): the angle by which the needle tilts down (or up) from horizontal. In Japan the end pointing north dips downward, by an angle of about 50 degrees.
MSHSCheck with a formula: how many metres is a 7.5-degree gap?
Multiplying an angular gap by the distance travelled converts it into a length. Here we calculate the "sideways drift" itself, which is the main subject of this article.
| In symbols | d = L × tan θ |
| In words | Sideways drift = distance travelled × tangent of the declination |
| Where it comes from | It comes from the definition of trigonometric ratios in a right triangle. Treating the distance travelled as the base and the declination as the angle at the starting point, the sideways drift is the opposite side. |
| Distance travelled L | 1000 m (1km on the map) |
| Declination θ (around Kanto) | Said to be 7.5 degrees west |
| Tangent of 7.5 degrees | Approximately 0.132 |
| Valley-to-valley spacing (typical in mountains) | 300 m |
| Sideways drift after 1km (m) | 1000 × 0.132 = 132 |
| Sideways drift after 5km (m) | 132 × 5 = 660 |
| How many valley-widths is that | 660 ÷ 300 = 2.2 |
That's about 132m after 1km, and about 660m after 5km. If one valley is about 300m wide, that's 2.2 times its width — enough to cross two ridges and end up in a completely different valley. Even a small angle, multiplied by distance, becomes a length that spans real terrain.
HSHS+What determines the direction the needle points?
HSThe needle tries to align with the horizontal component of Earth's magnetic field. Because Earth's field points diagonally downward, only its horizontal direction — what we call "needle north" on a map — is what the compass shows.
HS+The geomagnetism at any point can be expressed with three quantities: declination, inclination, and total field strength. These are called the three elements of geomagnetism. In the dipole approximation, which treats Earth as a single bar magnet, inclination and magnetic latitude are related by tan(inclination) = 2 × tan(magnetic latitude). How far the real values deviate from this approximation shows the size of the local distortion.
Univ.How is declination calculated worldwide?
Earth's overall magnetic field is expressed as an expansion in spherical harmonic functions. The standard model that determines these coefficients (Gauss coefficients) from observatories and satellite records worldwide is the International Geomagnetic Reference Field (IGRF). The declination shown on maps and instruments is calculated by feeding a location and date into this model. The theory of the flows that generate the field itself is called the geodynamo theory.
📖 For derivations and further reading: Geomagnetism (three elements and dipole approximation) ／ Dynamo theory
ResearchWhat's still not fully understood
- Why needle-north is moving faster. The north magnetic pole's drift is said to have sped up since the late 20th century, but what change in flow is happening inside the core is still debated.
- The weak region spreading over the South Atlantic. There's a patch of weak magnetic field stretching from the South Atlantic to Brazil, said to be growing. Whether this is a sign of an approaching geomagnetic reversal isn't settled.
- When and how a reversal would happen. Rocks record many past swaps of north and south, but there's still no established way to predict the timing or progress of the next one.
In other words, this article too only describes things "as currently understood." Declination values are updated with every new survey, so check the latest map before relying on one in practice.
Links to textbooks (by level)
| Level | Subject/Unit | Where in this article |
|---|---|---|
| MS | Science Field 1, "Current and Magnetic Fields" | Earth being a giant magnet, the needle pointing along the field |
| HS | Math I "Trigonometric Ratios" / Basic Physics "Magnetic Fields" | Calculating sideways drift with tangent, the horizontal-component idea |
| HS+ | Earth Science "Earth's Magnetic Field" | The three elements of geomagnetism, deviation from the dipole approximation |
| Univ. | Geomagnetism, Geodesy | Spherical harmonic expansion, International Geomagnetic Reference Field (IGRF) |
| Research | Deep Earth Physics | Magnetic pole drift, predicting geomagnetic reversals |
| ― | Everyday connection | Drawing a magnetic north line on a map for hiking, reading bearing notes on topo maps |
- Geospatial Information Authority of Japan (国土地理院), "Geomagnetic Survey / Magnetic Charts" (distribution of declination across Japan and its yearly change)
- Japan Meteorological Agency (気象庁), observation records from the Kakioka Magnetic Observatory (柿岡地磁気観測所) (long-term changes in declination, inclination, and total field strength)
- International Association of Geomagnetism and Aeronomy (IAGA), coefficient tables for the International Geomagnetic Reference Field (IGRF)
- Japanese Wikipedia, "Geomagnetism" (地磁気) (summary of the three elements, dipole approximation, and pole drift)
※This article is a general-audience science explainer. The figures given are approximate, meant to help convey the underlying mechanism. When heading into the mountains, follow the latest topographic maps, local guidance, and information from your municipality or relevant authorities.