Latitude and longitude to UPS
Converts polar coordinates (84° N and beyond, or 80° S and beyond) to Universal Polar Stereographic easting and northing.
UPS N: easting 2,000,000 m, northing 1,444,542.609 m.
- Hemisphere
- Easting
- Northing
- Grid convergence
- Point scale factor
- UTM
Provenance
- Computed by
- geodesy.ups.forward 1.0.0, core 0.1.0
- Model
- Polar stereographic, k0 = 0.994, false easting and northing 2,000,000 m
- Accuracy
- Exact to double precision
- Notes
- None
- Cites
- National Geospatial-Intelligence Agency, The Universal Grids and the Transverse Mercator and Polar Stereographic Map Projections, NGA.SIG.0012
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Polar stereographic, k0 = 0.994, false easting and northing 2,000,000 m
Accuracy: Exact to double precision
When to use this: Use this for a position in the polar caps, where UTM stops: north of 84 degrees or south of 80. It gives the UPS easting and northing a military grid reference, a polar chart or a navigation system expects, with the grid convergence you need to turn a true bearing into a grid one.
Limitations: UPS covers only the caps: north of 84 degrees and south of 80. Between those and the equator, UTM is the projection, and this refuses rather than extrapolating a polar projection into latitudes it distorts badly. Grid north here is the prime meridian, not the meridian through your point, so the convergence is the longitude itself and is large -- at 120 degrees east a grid bearing and a true bearing differ by 120 degrees. The scale is 0.994 at the pole and grows outward, reaching 1 near 81 degrees 6 minutes, so a distance measured on the grid is not a distance on the ground without it.
Worked example: 85° N on the prime meridian. Source: add-geodesy-suite scenario: 2,000,000 m E, 1,444,542.609 m N (±1 mm). It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Latitude
- 85 deg
- Longitude
- 0 deg
You get
- Zone
- 0
- Hemisphere
- N
- Easting
- 2,000,000 m
- Northing
- 1,444,542.609 m
- Grid convergence
- 0°
- Point scale factor
- 1.002555297
- UTM
- UPS N 2000000 1444542.609
Review: Not yet independently reviewed by a geodesist.
Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Checked against: 29 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- The Universal Grids and the Transverse Mercator and Polar Stereographic Map Projections, NGA.SIG.0012, National Geospatial-Intelligence Agency, NGA.SIG.0012_2.0.0_UTMUPS. Sections 3 (UTM zones, Norway and Svalbard exceptions) and 4 (UPS).
Terms
- UPS: Universal Polar Stereographic
- The polar companion to UTM, covering the areas north of 84° N and south of 80° S. Source: NGA.SIG.0012 UTM and UPS
- UTM: Universal Transverse Mercator
- A grid of 60 zones, each 6° of longitude wide, that turns latitude and longitude into eastings and northings in meters. Source: NGA.SIG.0012 UTM and UPS
Learn the concept: UTM coordinates explained