UPS to latitude and longitude

Model: Polar stereographic, k0 = 0.994

Accuracy: Exact to double precision

When to use this: Use this to turn a UPS easting and northing back into latitude and longitude: a polar grid reference off a chart, a logged position, or the output of a system that works in the polar caps. Say which hemisphere it came from, since the two caps use the same numbers.

Limitations: The hemisphere is required and is not guessed: 2,000,000 by 2,000,000 is the north pole and the south pole both, and every other pair of numbers is equally ambiguous. Near the pole a longitude is a very short distance on the ground, so a coordinate rounded to the metre fixes the longitude only loosely up there -- at 89.99 degrees a metre of easting is five thousand times the longitude it is at the equator. At the pole itself the longitude has no meaning at all.

Worked example: Back to 85° N. Source: add-geodesy-suite scenario inverse.

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: 26 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