UTM to latitude and longitude

Model: Transverse Mercator, 6th-order Krüger series (Karney 2011), k0 = 0.9996

Show your work

1. Off the central meridian

   x = easting − 500,000 m, the false easting the grid adds

   586,309.953 m − 500,000 m = 86,309.953 m

2. Zone's central meridian

   $${\lambda }_0=6°\times \mathrm{zone}-183°$$

   6° × 17 − 183° = -81°

3. Latitude

   φ from the transverse Mercator series, on this ellipsoid

   4,477,770.428 m north at zone 17 = 40.446111°

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Better than 5 nm within 3,900 km of the central meridian

When to use this: Use this when UTM coordinates arrive from a map, a data file, or a GPS set to a grid: give the zone, hemisphere, easting, and northing and it returns latitude and longitude, with the convergence and scale factor at that point. It is also the way to check a dataset's zone: converting a few coordinates and seeing where they land tells you quickly whether the zone recorded with them is the one they were computed in.

Limitations: The zone and hemisphere are part of the coordinate: the same easting and northing exist in every zone, so a missing or wrong zone produces a plausible position in the wrong place. The result carries the datum the coordinates were on, which this tool does not change, and points far from the central meridian carry more projection distortion. A northing alone does not say which hemisphere it belongs to, because southern coordinates carry a false northing; the hemisphere has to come with the coordinate.

Worked example: Pittsburgh from UTM. Source: add-geodesy-suite scenario: 40.446111°, -79.982222°. It is golden test vector v006, and every build checks the tool still gives its answer within its tolerance.

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.

Changes

• 2026-09-19, changed: Five more tools passed the stable verification bar: geodesic distance and destination (checked against GeographicLib's GeodTest), UTM forward and inverse (checked against exact transverse Mercator values), and the standard atmosphere (checked against a separately written implementation). Changelog

Checked against: 21 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

• Transverse Mercator with an accuracy of a few nanometers, Karney, C. F. F., Journal of Geodesy, Vol. 85, No. 8. pp. 475-485 (6th-order Krüger series).
• 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

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