geoprimsField-grade geospatial math

Latitude and longitude to UPS

Converts polar coordinates (84° N and beyond, or 80° S and beyond) to Universal Polar Stereographic easting and northing.

Go the other way: UPS to latitude and longitude →

0

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

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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
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

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