方眼北 vs 真北 vs 磁北
Three different "norths" are used in mapping and navigation: True North, Magnetic North, and Grid North. Confusing them is one of the most common sources of angular error in engineering surveys, military navigation, and directional drilling. Each has a distinct definition and a specific professional use case.
真北（地理的北）
True North points toward the geographic North Pole, the point where Earth's rotational axis meets the surface. All meridians of longitude converge at True North. It is fixed relative to the Earth's surface and is the reference for latitude/longitude and all geodetic measurements.
- Used in: astronomical observations, geodetic surveys, legal property descriptions
- Symbol: E(star symbol on compass roses)
磁北
Magnetic North is where a compass needle points, toward the magnetic pole in the Arctic. It does not coincide with True North and changes over time (secular variation). The angular difference between Magnetic North and True North is called magnetic declination.
- Magnetic declination varies from about -20 (west) to +20 (east) across the US
- Declination changes annually, old maps may have outdated declination values
- Source for current declination: NOAA's National Centers for Environmental Information
グリッド北
Grid North points toward the top of a map grid (e.g., a UTM or State Plane grid). Because these grids are flat projections of a curved Earth, they cannot be perfectly aligned with True North everywhere. The angular difference between Grid North and True North is called meridian convergence (or grid convergence).
- On a UTM map, Grid North and True North only coincide exactly at the central meridian of each zone
- At the edges of a UTM zone, convergence can be ±3
- In State Plane coordinates, convergence depends on the specific zone and location
子午線収束角の重要性
Meridian convergence is the angle between Grid North and True North at a specific location. It is calculated as:
γ = (λ - λ₀) ±sin(φ)
Where λ is longitude, λ₀ is the central meridian, and ρEis latitude. At high latitudes (e.g., Alaska, Scandinavia), convergence grows larger and causes serious errors if ignored.
—Read Full Case Study
実用変換テーブル
| Application | Use This "North" | Notes |
|---|---|---|
| Compass navigation | Magnetic North | Apply declination correction for true bearing |
| GPS / coordinate systems | True North | All lat/long bearings are relative to True North |
| UTM / State Plane surveys | Grid North | Apply convergence correction for True North |
| Directional drilling | True North | ISCWSA standards require convergence correction |
| Military MGRS | Grid North | MGRS is based on the UTM grid |
| Legal property descriptions | True North | Metes and bounds use true bearings |
グリッド北→真北変換の計算方法
- Determine your UTM zone and central meridian (e.g., Zone 17N: 81W)
- Calculate the longitude difference: Δλ = your longitude - central meridian
- Apply: γ = Δλ ±sin(φ) [in degrees, where ρE= latitude]
- Positive γ = Grid North is east of True North
Convert coordinates between UTM and Lat/Long, tool includes zone information:
—Lat/Long to UTM ConverterFAQ
Does Google Maps use Grid North or True North?
Google Maps displays a north-up orientation that approximates True North at the center of the map. Because the underlying Web Mercator (EPSG:3857, valid -85.05° to +85.05°) projection aligns grid lines with True North at the equator, grid north and true north diverge at higher latitudes.
How large can meridian convergence get?
In UTM, convergence can reach ±3 at zone edges at moderate latitudes. At high latitudes (Alaska, Arctic regions), it can exceed 5. In State Plane coordinates, it is typically smaller because zones are narrower.
Do I need to apply convergence correction for GIS work?
For GIS work using angular measurements (bearings, azimuths), yes. For plotting coordinates only, convergence is already accounted for in the projection math. The issue arises when mixing angular measurements from field instruments (referenced to Magnetic or True North) with grid-based coordinate systems.
What is the magnetic declination in the US?
US magnetic declination ranges from about -20 in the Pacific Northwest to +15 in Maine and the Northeast. The agonic line (zero declination) runs roughly through the eastern Midwest. Always check the NOAA NCEI Geomagnetic Calculator for current, location-specific values.
See also: Coordinate Reference Standards | 測量における縮尺係数 (Scale Factor) | UTM Anti-Collision Failure Case
米国平面直角座標系（SPCS）変換 & ガイド
各州固有の正角投影グリッドからGPS WGS84への高精度測量・工学座標変換。
地殻変動と再施工リスク：NAD83 vs WGS84の累積誤差
北米プレートは年間約2cm移動するため、NAD83(2011)とWGS84(G1762)は現在2.2メートル以上乖離しています。 高精度なNAD83地籍杭打ちに「標準的な」GPS WGS84座標を使用したことで、基礎のやり直しやインフラの配置ミスによる5万ドルの専門家責任賠償請求が発生しています。