How this calculator works
The Universal Transverse Mercator grid divides the world into 6-degree longitudinal zones, each numbered from 1 to 60. A transverse Mercator projection is centred on each zone, so distortion stays small within the zone. Easting is measured from a false origin 500,000 m west of the central meridian, and southern latitudes add 10,000,000 m to the northing so the numbers stay positive. The latitude band letter is a separate 8-degree label and is not part of the grid coordinates.
Formula
zone = floor((longitude + 180) / 6) + 1, with the Norway and Svalbard exceptions. Within the zone, easting = 500,000 + k0 N [A + (1 - T + C) A^3 / 6 + (5 - 18T + T^2 + 72C - 58e'^2) A^5 / 120] and northing = k0 [M + N tan(phi) (A^2 / 2 + (5 - T + 9C + 4C^2) A^4 / 24 + (61 - 58T + T^2 + 600C - 330e'^2) A^6 / 720)], with a false northing of 10,000,000 m in the south. Here N is the radius of curvature in the prime vertical, T = tan^2(phi), C = e'^2 cos^2(phi), A = (lambda - lambda0) cos(phi) and M is the meridian arc. The WGS84 ellipsoid uses a = 6,378,137 m and 1/f = 298.257223563; k0 = 0.9996.
Worked example
London at 51.5074 N, 0.1278 W falls in zone 30U. The calculation gives an easting of about 699,317 m and a northing of about 5,710,164 m. In degrees minutes seconds, 51°30'26.64"N 0°07'40.08"W is the same point.
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Frequently asked questions
Why does UTM stop at 84 degrees north and 80 degrees south?
The polar caps use the Universal Polar Stereographic grid instead, because a transverse Mercator projection becomes badly distorted near the poles.
Does the zone letter change the easting or northing?
No. The letter is a latitude band label that makes the zone name easier to read. It does not alter the grid coordinates.
How accurate is this conversion?
The series used here is accurate to about a metre within a zone on the WGS84 ellipsoid. Survey-grade work should use the official projection software and a stated datum and epoch.