UTM and MGRS

NGA's UTM and MGRS · checked against GeographicLib's GeoConvert

Published · 1682 cases

What it is

UTM splits the world into 60 zones, each 6° of longitude wide, and flattens each onto its own grid in metres: an easting and a northing. MGRS is the military form of the same grid. It names the zone, a latitude band and a 100 km square, then gives the easting and northing inside that square, with more digits for more precision.

Part of `10U DU 85234 71665`	Means
`10`	Zone 10, 126° W to 120° W
`U`	Latitude band U, 48° N to 56° N
`DU`	The 100 km square
`85234 71665`	Easting and northing in that square: five digits each is 1 m

A reference names the south-west corner of the square the point is in. So each digit is truncated, never rounded. This is the most common mistake in MGRS code.

The test data writes references as GeographicLib does, with no spaces and the zone padded to two digits: 10UDU8523471665. How to space them for a person is the display’s call.

Operations

Operation	Gives
`toUtm`	UTM from a latitude and longitudeIn: `latitudeInDegrees`, `longitudeInDegrees` Out: `zone`, `hemisphere`, `eastingInMeters`, `northingInMeters`, `convergenceInDegrees`, `pointScale`
`fromUtm`	A latitude and longitude from UTMIn: `zone`, `hemisphere`, `eastingInMeters`, `northingInMeters` Out: `latitudeInDegrees`, `longitudeInDegrees`
`toMgrs`	An MGRS reference from a latitude and longitudeIn: `latitudeInDegrees`, `longitudeInDegrees`, `precisionInDigits` Out: `mgrs`
`fromMgrs`	The latitude and longitude of the reference's square's centreIn: `mgrs` Out: `latitudeInDegrees`, `longitudeInDegrees`
`parse`	A latitude and longitude from a typed coordinate: DD, DDM, DMS, UTM or MGRSIn: `text` Out: `latitudeInDegrees`, `longitudeInDegrees`

Fields

Field	Meaning
`latitudeInDegrees`	−90 to 90, WGS84, north positive
`longitudeInDegrees`	−180 to 180, WGS84, east positive. 180 is the same meridian as −180, in zone 1.
`zone`	1 to 60; 0 for UPS, from 84° N and beyond 80° S. Exactly 80° S is still UTM.
`hemisphere`	north or south. The equator is north.
`eastingInMeters`	In the zone, with 500,000 on its central meridian. UPS puts 2,000,000 at the pole.
`northingInMeters`	From the equator in the north, from 10,000 km south of it in the south. UPS puts 2,000,000 at the pole.
`convergenceInDegrees`	Grid convergence: the angle clockwise from true north to grid north
`pointScale`	The grid's scale at the point: 0.9996 on a UTM central meridian, 0.994 at a pole
`precisionInDigits`	0 to 5 digits each for easting and northing: 0 names the 100 km square, 5 is 1 m
`mgrs`	GeographicLib's form: the zone padded to two digits, the band, the square's two letters and the digits, with no spaces, like 04QFJ1234567890. UPS has no zone: ZAH0000000000. fromMgrs also takes an unpadded zone and lower case.
`text`	A coordinate as a person types it: decimal degrees; degrees and minutes, or degrees, minutes and seconds, with ° ' " or colons; hemisphere letters before or after, and either order when lettered. Or UTM as 10n 491221 5458889, or MGRS.

Edge cases

Case	What it tests
`edge-to-utm-norway-32v`toUtm	Norway: at 60° N, 5° E is zone 32, not 31.
`edge-to-utm-norway-32v-west-edge`toUtm	Zone 32V is widened west to 3° E.
`edge-to-utm-norway-31v-west-of-edge`toUtm	Just west of 3° E: still zone 31.
`edge-to-utm-norway-32v-south-edge`toUtm	Exactly 56° N is band V, so the Norway rule applies.
`edge-to-utm-norway-31u-south-of-edge`toUtm	Just south of 56° N is band U: zone 31.
`edge-to-utm-norway-31w-north-of-band`toUtm	Exactly 64° N is band W: zone 31 again.
`edge-to-utm-svalbard-31x`toUtm	Svalbard: zone 31X runs to 9° E.
`edge-to-utm-svalbard-33x-west`toUtm	Zones 32X, 34X and 36X don't exist: 9° E is 33X.
`edge-to-utm-svalbard-37x`toUtm	33° E starts zone 37X.
`edge-to-utm-svalbard-32w-below-band`toUtm	Just below 72° N is band W: the Svalbard rule doesn't apply.
`edge-to-utm-utm-last-north`toUtm	Just below 84° N: still UTM.
`edge-to-utm-ups-first-north`toUtm	Exactly 84° N is UPS, zone 0.
`edge-to-utm-utm-last-south`toUtm	Exactly 80° S is still UTM.
`edge-to-utm-ups-first-south`toUtm	Just past 80° S: UPS.
`edge-to-utm-antimeridian-east`toUtm	180° is the same meridian as −180°: zone 1.
`edge-to-utm-zone-60`toUtm	Just west of 180°: zone 60.
`edge-to-utm-equator`toUtm	The equator is north, with northing 0.
`edge-to-utm-just-south-of-equator`toUtm	A hair south: northing just under 10,000,000.
`edge-to-utm-north-pole`toUtm	The pole is UPS easting and northing 2,000,000, scale 0.994.
`edge-to-utm-central-meridian`toUtm	On the central meridian: easting exactly 500,000, convergence 0, scale 0.9996.
`edge-to-mgrs-equator`toMgrs	Northing 0 at the equator: 00000.
`edge-to-mgrs-north-pole`toMgrs	UPS has no zone number: ZAH.
`edge-from-utm-truncation`fromUtm	The point the page's diagram draws: easting 85234.9, northing 71665.8 in its square.
`edge-to-mgrs-truncation-5`toMgrs	Truncated, not rounded: 85234 71665, not 85235 71666.
`edge-to-mgrs-truncation-3`toMgrs	Three digits truncate further: 852 716.
`edge-from-mgrs-unpadded-zone`fromMgrs	4Q reads the same as 04Q.
`edge-from-mgrs-lower-case`fromMgrs	Lower case reads the same.
`edge-from-mgrs-100-km-square`fromMgrs	No digits: the centre of the 100 km square.
`parse-longitude-first`parse	Hemisphere letters say which is which, so the longitude can come first.
`parse-degrees-minutes-seconds`parse	Degrees, minutes and seconds with ° ' and " marks.
`parse-colons`parse	Colons instead of marks.
`parse-utm`parse	Three parts: a UTM zone and hemisphere, easting and northing.
`parse-mgrs`parse	One part: an MGRS reference, read as its square's centre.
`invalid-from-utm-easting-1500-km`fromUtm	Past the zone's easting limits: outOfRange.
`invalid-from-mgrs-odd-digits`fromMgrs	An odd number of digits: invalidInput.
`invalid-parse-two-latitudes`parse	Both lettered N: invalidInput.
`invalid-to-mgrs-precision-6`toMgrs	Past this file's 0 to 5 digits.

Their inputs and expected values are in vectors.json; search for the case's id.

For agents

Implement the Transverse Mercator projection with the Krüger series to sixth order in n, as in Karney (2011), on WGS84, with a scale of 0.9996 on each zone’s central meridian and false easting 500,000 m (and false northing 10,000,000 m in the south). Simpler textbook formulas drift near zone edges and fail the 1 mm tolerance. Beyond it, use Universal Polar Stereographic, zone 0, with scale 0.994 at the pole and false easting and northing 2,000,000 m. Apply the Norway and Svalbard zone exceptions. For MGRS, truncate the digits, never round, and read a reference back as the centre of its square. GeographicLib’s GeoConvert is the reference: match its choices, including where UPS starts. Pass every case in vectors.json within its tolerance.

Test data

vectors.json holds 1682 cases, published 2026-09-29. Earth model: WGS84. How to read it: Test data format.

Operation	Cases
`toUtm`	427427 reference · 26 edge · 9 polar · 1 invalid
`fromUtm`	403403 reference · 1 edge · 3 polar · 2 invalid
`toMgrs`	430429 reference · 29 edge · 9 polar · 1 invalid
`fromMgrs`	408408 reference · 6 edge · 3 polar · 2 invalid
`parse`	1414 reference · 11 edge · 3 invalid

Tags say where each value came from: what they mean.

Field	Tolerance
`latitudeInDegrees`	± 0.0000001
`longitudeInDegrees`	± 0.0000001
`eastingInMeters`	± 0.001
`northingInMeters`	± 0.001
`convergenceInDegrees`	± 0.000001
`pointScale`	± 0.0000001

Every other field is compared exactly.

Implementations

Repo	Status
gshaw/algorithms-swiftSwift	Passes

Each is a public repo that runs this page's test data with mise run test. See how implementations work.

Source

Standard	Universal Grids and Grid Reference Systems, NGA.STND.0037National Geospatial-Intelligence Agency · Public domain
Method	Transverse Mercator with an accuracy of a few nanometersC. F. F. Karney, Journal of Geodesy 85, 475–485 (2011). https://doi.org/10.1007/s00190-011-0445-3
Reference program	GeoConvert, GeographicLib 2.7Charles Karney. Every call and its output is in /utm-mgrs/sources/geoconvert.txt · MIT