UTM ↔ Latitude/Longitude Converter

The structure of a UTM coordinate

A complete UTM position has four parts: a zone number (1–60), a band letter (C–X excluding I and O), an easting in metres, and a northing in metres. The Empire State Building, in canonical form, reads:

18T 585628 mE 4511322 mN
│  │ │      │ │       │
│  │ │      │ │       └ northing label
│  │ │      │ └ northing in metres (from equator)
│  │ │      └ easting label
│  │ └ easting in metres (offset from 500,000 false easting)
│  └ band letter (T = 40°N to 48°N latitude)
└ zone number (1–60, indicating which 6°-wide longitude strip)

Each zone is 6° of longitude wide. Zone 1 starts at 180°W; zone 60 ends at 180°E. The zone number for a given longitude is floor((lon + 180) / 6) + 1. The band letter partitions latitude into 20 strips, 8° tall each, except band X which is 12° tall (covering 72°N–84°N). Bands C–M sit in the Southern hemisphere; N–X in the Northern.

How UTM ↔ lat/lon math works

The Transverse Mercator projection wraps a cylinder around the Earth along a chosen meridian (the zone's central meridian), then projects every point onto that cylinder. Unrolled flat, the central meridian becomes a vertical line at easting 500,000; everywhere else in the zone gets a curved-but-tractable transformation. The full forward and inverse formulas are 6th- order series in WGS-84 ellipsoidal parameters; the canonical reference is USGS Snyder PP 1395 (1987), still the most cited derivation in geodetic literature.

Ten worked examples — both directions

The Greenwich row is a useful sanity check: zone 30's central meridian sits at 3°W, so a point at longitude 0° is about 3° east of the central meridian. The easting comes out near 708,287 m — well east of the 500,000 m central-meridian value — confirming the false-easting offset is being applied as expected. Cross the prime meridian by half a metre and the result jumps into zone 31, easting near 291,800 m on the western edge of that zone. Behaviour at zone boundaries is the most common surprise in UTM workflows.

Misconceptions worth getting straight

"Northing and latitude are the same thing"

No. Northing is metres on a flat projection of a 6°-wide Earth strip; latitude is angular degrees from the equator. They track each other closely (one degree of latitude is ~111,320 m), but they aren't identical. The easting/northing pair is Cartesian on the projection; lat/lon is angular on the ellipsoid.

"You can subtract two UTM coordinates to get a distance"

Inside the same zone, yes — that's a key reason UTM exists. √((ΔE)² + (ΔN)²) gives the planar distance to about 1 part in 2,500 worst-case. Across zones, no — the projections differ. For cross-zone distance, convert both points to lat/lon first and use Haversine or Vincenty.

"The band letter just tells you the hemisphere"

It encodes more than that. Bands C–M = Southern; N–X = Northern, yes — but they also identify a specific 8° latitude strip, which most GIS software uses for sanity-checking input. A UTM string with the wrong band letter for its northing will be caught by validators.

"UTM is a coordinate system"

UTM is a projected coordinate system built on top of a geographic coordinate system (WGS-84 lat/lon, in this implementation). The distinction matters: changing the underlying datum (e.g., NAD27 vs WGS-84) changes the UTM result by up to ~200 m. Almost all modern data uses WGS-84 or its near-equivalents (NAD83, ITRF), but legacy NAD27 data is still common in the United States and Canada.

"MGRS is the same as UTM with letters"

Closely related, not identical. MGRS is built on UTM south of 84°N (and UPS north of it), but it adds a 100-km grid-square letter pair, then expresses the in-square offset in fewer digits (with progressively coarser precision). MGRS is the military-grid expression; UTM is the raw metric one.

When to use UTM, when not to

How to verify a UTM coordinate

Three sanity checks any UTM result should pass:

1. Easting is between ~166,000 and ~834,000 m.Outside this range, the point is in the wrong zone (and a re-projection to the neighbouring zone is needed) or the false easting was forgotten.
2. Northing matches the band letter. Bands C–M require Southern-hemisphere northings (1,116,000 to 10,000,000 m); N–X require Northern (0 to 9,329,000 m). Cross-checking is a common validator step.
3. Round-trip the conversion. Convert your UTM back to lat/lon, and confirm it matches your starting lat/lon to within a millimetre. Any larger discrepancy is a sign of either zone error or datum mismatch.

For complex projects — mixed UTM/lat-lon data, or any work crossing zones — keep a copy of the lat/lon (WGS-84) as the authoritative source. UTM is a derived representation; lat/lon is the underlying truth.

How this converter is built

The math runs entirely in the browser: forward and inverse formulas live in src/lib/coords/utm.ts, implementing Snyder PP 1395 §8 verbatim with the WGS-84 ellipsoid. Direction is auto-detected from the input string — a regex match on <digits><letter> <digits> <digits>triggers the UTM-to-lat/lon path; anything else is parsed as lat/lon. The map below the converter uses MapLibre GL with MapTiler tiles and renders the result point as a draggable pin. Clicking the map sets the input to that point's decimal-degree coordinates and re-runs the conversion. The deep report sub-fetches nearest place (Mapbox v6, server-side proxy with no-store cache) and elevation (USGS 3DEP for US, OpenTopoData SRTM30m elsewhere) — both per CLAUDE.md §19.2 and §19.4. No coordinates are ever logged or retained.