Latitude and longitude to UTM

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

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1. Zone

   zone = ⌊(lon + 180) / 6⌋ + 1, unless one is given

   -79.982222° longitude = zone 17

2. Central meridian

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

   6° × 17 − 183° = -81°

3. Easting

   x from the transverse Mercator series, plus the 500,000 m false easting

   1.017778° east of -81° = 586,309.953 m

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 work is done on a metric grid: UTM easting and northing for a latitude and longitude, with the zone, the grid convergence between grid north and true north, and the point scale factor. It handles the Norway and Svalbard zone exceptions and can force a neighboring zone when a project spans a boundary.

Limitations: UTM is a projection, so distances and directions carry scale distortion that the scale factor quantifies, and a grid bearing is not a true bearing by the amount of the convergence. Zones are six degrees wide and coordinates do not carry their zone, so a easting and northing without it is ambiguous. The datum is whatever the input's was.

Worked example: Pittsburgh. Source: add-geodesy-suite scenario: 17N 586,309.953 m E, 4,477,770.428 m N (±1 mm). It is golden test vector v001, 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
• 2026-09-19, result change: UTM forward is now stable, so its results no longer carry the EXPERIMENTAL_TOOL warning. The nonstandard-zone warning moved to the first position; no numbers changed. 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