UTMの仮想東距と仮想北距の解説
When you look at a UTM (ユニバーサル横メルカトル図法) coordinate, the numbers are usually very large, like Easting: 423,000m and Northing: 4,000,000m. These numbers look random until you understand how the UTM grid shifts its origin to avoid negative numbers.
False Easting: 500,000 meters is artificially added to every X-coordinate.
False Northing: 10,000,000 meters is artificially added to Southern Hemisphere Y-coordinates.
フォルスイースティングを使う理由
Every UTM zone is 6 degrees of longitude wide, with a "Central Meridian" directly in the middle. If the Central Meridian was assigned an X-value of 0, everything to the west of the line would have a negative coordinate.
To prevent surveyors and military personnel from mixing up positive and negative signs (which causes severe mapping errors), the Central Meridian is arbitrarily given a value of 500,000 meters East. This shift is the False Easting.
- If your Easting is > 500,000, you are east of the center of the zone.
- If your Easting is < 500,000, you are west of the center of the zone.
- Because a UTM zone is only about 660km wide at the equator, the Easting value will never reach 0, nor will it exceed 1,000,000. It is always a 6-digit number.
フォルスノーシングを使う理由
In the Northern Hemisphere, the Northing value starts at 0 meters exactly at the Equator and counts upward toward the North Pole. No False Northing is needed.
In the Southern Hemisphere, counting down from 0 at the Equator would result in negative numbers. To fix this, the Equator is arbitrarily assigned a value of 10,000,000 meters North. As you travel south toward Antarctica, the number decreases (e.g., 9,000,000, 8,000,000).
北半球/南半球の衝突問題
If you have a UTM coordinate like Zone 18, Northing: 5,000,000, you do not actually know where you are unless the hemisphere is specified.
- Zone 18N (North): You are 5 million meters north of the Equator (roughly New York / Canada).
- Zone 18S (South): You are 5 million meters south of the Equator (roughly Chile / Argentina, because 10,000,000 - 5,000,000 = 5,000,000m south).
Test the math yourself. Convert a latitude in the Northern and Southern hemisphere to see the Northing shift.
—Interactive Lat/Long to UTM ConverterMGRS vs UTMのフォルスオリジン
The Military Grid Reference System (MGRS) removes the need to understand False Eastings and Northings by replacing these massive 6 and 7-digit numbers with 100km square letter designations. The 100km letters intrinsically encode the hemisphere and the offset, making MGRS much safer for human communication.
FAQ
What does 500,000mE mean?
It means 500,000 meters Easting. If a coordinate has this value, it lies exactly on the central meridian of its UTM zone. It does not literally mean 500 kilometers east of a physical location, it is an arbitrary grid shift.
Does State Plane use False Eastings?
Yes. The US State Plane Coordinate System (SPCS) also uses massive False Eastings (e.g., 2,000,000 feet) and False Northings to ensure all values within a state are positive numbers.
Why did my data snap to the Equator?
If your UTM Easting/Northing data appears near 0,0 (off the coast of West Africa), your software misread the UTM projection as a Lat/Long projection (EPSG:4326). It attempted to plot a 500,000 Easting as 500,000 degrees longitude, which fails and defaults to 0.
See also: How to Read MGRS | EPSG:4326 vs 3857
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。
誤った測地系（データム）の指定や、グリッド・地上補正（Grid-to-Ground）を適用しない座標変換は、1〜400mの位置ズレを引き起こします。これは測量過失請求や施工紛争の代表的な原因です。
縮尺係数の歪みとSPCSの工学的責任
標高差の大きい山岳SPCSゾーン（コロラド州やカリフォルニア州など）では、合成縮尺係数の誤差が1kmあたり15cmに達することがあります。グリッド座標（投影平面）を地上距離として補正なしで扱うと、重大な施工ミスや杭位置の誤認につながります。