Latitude/Longitude to UTM Converter (and UTM to Lat/Long) on WGS 84
Convert latitude/longitude (decimal or DMS) to UTM zone, easting and northing on WGS 84, or UTM back to lat/long, with MGRS, scale factor and convergence.
How it works
Zone = floor((longitude + 180) ÷ 6) + 1 (Norway and Svalbard exceptions) · Central meridian λ0 = 6 × zone − 183 · Transverse Mercator on WGS 84 (a = 6,378,137 m, f = 1/298.257223563) with the Krüger series to order n⁶: ξ = ξʹ + Σ αj sin 2jξʹ cosh 2jηʹ, η = ηʹ + Σ αj cos 2jξʹ sinh 2jηʹ · Easting = 0.9996 × A × η + 500,000 m · Northing = 0.9996 × A × ξ (+ 10,000,000 m south of the equator)
The Universal Transverse Mercator (UTM) system splits the world between 80° S and 84° N into 60 zones, each 6° of longitude wide, and flattens each one with its own transverse Mercator projection. A position becomes a zone number plus two distances in metres: the easting, measured from a line 500,000 m west of the zone’s central meridian so it is never negative, and the northing, measured from the equator (with 10,000,000 m added in the southern hemisphere). The central meridian is scaled by 0.9996 so that distortion stays within about 1 part in 1,000 across the zone. Because UTM coordinates are in metres on a flat grid, distances and areas can be measured with a ruler and Pythagoras, which is why topographic maps, surveyors, GIS and search-and-rescue teams use them. This converter uses the Krüger series to sixth order (Karney’s method), which is accurate to a few nanometres within the zone, far beyond the 1–2 m accuracy of the WGS 84 datum itself. It handles the Norway and Svalbard zone exceptions, accepts decimal degrees or degrees-minutes-seconds with N/S/E/W, and also converts UTM back to latitude and longitude. It adds the MGRS (military grid) reference, the point scale factor and the grid convergence (the angle between grid north and true north). Unlike the UTM zone calculator, which only names the zone, this page gives the full coordinates in both directions. Results are on WGS 84, which matches GPS; for maps on older datums such as NAD27 or ED50, transform the datum first.
Worked example
The CN Tower in Toronto is at 43°38′33.24″ N, 79°23′13.7″ W, or 43.6425667, −79.387139. Its zone is floor((−79.387139 + 180) ÷ 6) + 1 = 17, whose central meridian is 17 × 6 − 183 = −81°, so the tower is 1.612861° east of it. The transverse Mercator projection gives x = 130,084.30 m and y = 4,833,438.55 m, so the easting is 630,084.30 m and the northing 4,833,438.55 m: UTM 17N 630084 4833438, or MGRS 17T PJ 30084 33438. The point scale factor there is 0.999808 (a grid distance is 0.02% shorter than on the ground), and grid north is 1.1133° east of true north.
Sources: Movable Type Scripts (C. Veness): UTM / MGRS conversion using Karney’s method (52.2° N, 0.12° E example) · Wikipedia: Universal Transverse Mercator coordinate system (CN Tower example, zone exceptions) · Omni Calculator: Lat long to UTM converter
Frequently asked questions
How do I convert latitude and longitude to UTM?
Find the zone with floor((longitude + 180) ÷ 6) + 1, then project the point with the transverse Mercator formulas on the WGS 84 ellipsoid using the zone’s central meridian, a scale of 0.9996 and a false easting of 500,000 m (plus a false northing of 10,000,000 m in the southern hemisphere). The calculator does all of this; for example 52.2° N, 0.12° E is 31N 303189 5787193.
What are easting and northing?
Easting is the distance in metres east of a false origin 500,000 m west of the zone’s central meridian, so values run from about 166,000 to 834,000 m at the equator. Northing is the distance north of the equator, or north of a point 10,000,000 m south of the equator in the southern hemisphere.
How do I know which UTM zone I am in?
Each zone covers 6° of longitude, starting with zone 1 at 180° to 174° W and increasing eastward. Divide (longitude + 180) by 6, drop the decimals and add 1. Southwest Norway and Svalbard have special zones, which the calculator applies.
Is UTM the same as MGRS?
MGRS is built on UTM. It adds a latitude band letter to the zone, replaces the leading digits of the easting and northing with a two-letter 100 km square, and keeps the remaining digits, e.g. 31U CT 03189 87193 for 31N 303189 5787193.
Which datum does this converter use?
WGS 84, the datum of GPS. NAD83 in North America, ETRS89 in Europe and SIRGAS in Latin America agree with it to within about a metre or two for most uses. Older local datums such as NAD27, ED50 or PSAD56 differ by up to several hundred metres and need a datum transformation first.
Why do UTM coordinates not work near the poles?
The transverse Mercator projection is only defined up to 84° N and 80° S in the UTM system. Polar regions use the Universal Polar Stereographic (UPS) grid instead.
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This calculator is for educational purposes. Double-check important results before acting on them.