Latitude/Longitude to UTM — WGS 84 Converter

Background.

Latitude and longitude place a point on the curved Earth in degrees, which is awkward for anything measured on the ground: a degree of longitude spans about 111 km at the equator and shrinks to nothing at the poles. Universal Transverse Mercator swaps the angles for metres. A point near the centre of Nairobi at 1.2864°S, 36.8172°E becomes 37S 257110.720 E 9857710.001 N, a position in a flat grid where the distance between two nearby points is simple Pythagoras.

The grid covers the world from 80°S to 84°N in sixty zones, each six degrees of longitude wide and numbered eastward from 180°W. Within a zone the ellipsoid is projected onto a cylinder that touches it along the zone's central meridian, and the result is scaled by 0.9996 to spread the distortion: distances come out 0.04 percent short on the central meridian, true along two lines roughly 180 km either side, and about 0.1 percent long at the zone's edge on the equator. A false easting of 500,000 m keeps every easting positive, and in the southern hemisphere 10,000,000 m is added to the northing for the same reason.

The converter works in both directions. Forward mode picks the standard zone for you, including the exceptions around south-west Norway and Svalbard; reverse mode takes zone, hemisphere, easting and northing and returns decimal degrees. The arithmetic is John Snyder's transverse Mercator power series from USGS Professional Paper 1395, evaluated on the WGS 84 ellipsoid.

WGS 84 is the datum GPS receivers report. Coordinates on an older datum, such as Arc 1960 in East Africa or NAD27 in North America, can look almost identical while describing a point many metres away, and no datum shift is applied here, so confirm your source is WGS 84 before converting.

What is latitude/longitude to utm calculator?

UTM is a set of transverse Mercator grids, one for each six-degree zone in each hemisphere, all built on the same ellipsoid with the same scale factor and false origins. A UTM coordinate therefore has four parts: zone number, hemisphere, easting and northing. The easting is metres east of a line 500 km west of the zone's central meridian; the northing is metres north of the equator, or of a line 10,000 km south of it in the southern hemisphere. Drop the zone or the hemisphere and the same easting and northing could name a point in any of 120 grids.

How to use this calculator.

1. 01Check that your coordinates are WGS 84, the datum of GPS and most web maps.
2. 02For latitude/longitude to UTM, enter decimal degrees with south and west as negative numbers, latitude between −80 and 84. Convert degrees, minutes and seconds to decimals first.
3. 03For UTM to latitude/longitude, enter the zone (1 to 60), the hemisphere, the easting (100,000 to 900,000 m) and the northing (0 to 10,000,000 m).
4. 04Keep the zone and hemisphere with every easting and northing you record, and never subtract coordinates taken from different zones.

The formula.

The zone is floor((longitude + 180) ÷ 6) + 1, held at 60 for 180°E. Between 56°N and 64°N, longitudes from 3°E to 12°E go to zone 32; between 72°N and 84°N only zones 31, 33, 35 and 37 are used, covering 0–9°E, 9–21°E, 21–33°E and 33–42°E. The zone's central meridian is λ₀ = 6 × zone − 183 degrees. Snyder's forward series then works with A = (λ − λ₀) cos φ, the east-west offset scaled to the latitude; N, the ellipsoid's radius of curvature across the meridian; T = tan² φ; C = e′² cos² φ; and M, the distance along the meridian from the equator, expanded to the sixth power of the eccentricity. Easting = 500,000 + 0.9996 × N × (A + (1 − T + C)A³ ÷ 6 + a fifth-order term), and northing = 0.9996 × (M + N tan φ × (A² ÷ 2 + fourth- and sixth-order terms)), plus 10,000,000 in the south. The inverse removes the false origins, finds the footpoint latitude from a series in the rectifying latitude μ, and applies Snyder's inverse terms. The ellipsoid is WGS 84: a = 6,378,137 m and 1/f = 298.257223563. These series are designed for points within a zone and lose accuracy far beyond its edges, which automatic zone selection avoids.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Snyder (1987), Map Projections — A Working Manual, USGS Professional Paper 1395: the transverse Mercator forward and inverse series this page evaluates.
2. [2]NOAA Manual NOS NGS 5 publishes UTM scale, zone and false-coordinate parameters.
3. [3]NOAA NGS NCAT USNG service provides independent UTM conversion examples used to check this calculator's results.