UTM Coordinate Converter

Understanding the UTM system

The Universal Transverse Mercator (UTM) coordinate system is a projected, meter-based grid used for mapping and navigation. Instead of describing a location with angles (latitude/longitude), UTM represents positions as Easting (meters east of a reference) and Northing (meters north of a reference) within a numbered zone.

UTM divides the Earth into 60 zones, each 6° of longitude wide. Within a zone, a Transverse Mercator projection is used so that distortion is kept small near the zone’s central meridian—making UTM practical for local to regional mapping, distance measurement, and fieldwork.

Zones, central meridians, and hemispheres

Given longitude λ in degrees, the standard UTM zone number (1–60) is:

Zone = ⌊(λ + 180) / 6⌋ + 1

The central meridian of that zone (in degrees) is:

λ₀ = 6 × Zone − 183

UTM northings differ by hemisphere because of a false origin:

• Northern hemisphere: Northing starts at 0 m at the equator.
• Southern hemisphere: A false northing of 10,000,000 m is added so values remain positive.

UTM eastings also include a false easting of 500,000 m at the central meridian, so eastings stay positive across the zone.

Datum and projection constants (WGS84)

This converter assumes the WGS84 ellipsoid, which is also the default reference for GPS. Key constants are:

• Semi-major axis: a = 6378137 m
• Flattening: f = 1/298.257223563
• First eccentricity squared: e² = f(2 − f)
• UTM scale factor at central meridian: k₀ = 0.9996

Forward conversion (Latitude/Longitude → UTM): formulas

At a high level, the forward Transverse Mercator projection computes a meridional arc length and applies series expansions based on latitude and the longitude difference from the central meridian. Common intermediate terms include:

• φ: latitude in radians
• λ: longitude in radians
• λ₀: central meridian in radians
• A = (λ − λ₀) · cos φ
• T = tan² φ
• C = e′² · cos² φ, where e′² = e² / (1 − e²)
• ν = a / √(1 − e² sin² φ) (radius of curvature in the prime vertical)
• M: meridional arc length from the equator to latitude φ

The resulting UTM coordinates are easting E and northing N (meters), including the standard false easting/northing. A commonly cited truncated series form is:

Implementations typically use well-tested geodesy series expansions for M (the meridional arc) and may include additional higher-order terms depending on desired accuracy.

Interpreting the results

When you convert latitude/longitude to UTM, you should interpret the output as:

• Zone number (1–60): which 6° longitudinal band you are in.
• Hemisphere (N/S): determines whether the 10,000,000 m false northing is applied.
• Easting (m): meters east of the zone’s central meridian, with a 500,000 m false easting.
• Northing (m): meters north of the equator (plus false northing in the southern hemisphere).

As a quick sanity check, eastings in a zone are commonly near a few hundred thousand meters; values far outside a typical range may indicate the wrong zone, wrong sign on longitude, or coordinates outside normal UTM coverage.

Worked example (Lat/Lon → UTM)

Suppose you have a GPS coordinate near San Francisco:

• Latitude: 37.7749°
• Longitude: −122.4194°

Compute the zone:

• Zone = ⌊(−122.4194 + 180) / 6⌋ + 1 = ⌊57.5806 / 6⌋ + 1 = 9 + 1 = 10
• Central meridian λ₀ = 6×10 − 183 = −123°

The output will be reported as Zone 10N with an easting and northing in meters. (Exact numeric easting/northing depends on the full series implementation and rounding.)

Zone reference table (examples)

Limitations & assumptions

• Latitude coverage: Standard UTM is defined for approximately 84°N to 80°S. Near the poles, UPS (Universal Polar Stereographic) is typically used instead.
• Datum/ellipsoid: Results assume WGS84. If your data uses another datum (e.g., NAD83 or local datums), coordinates can differ by meters or more.
• Zone boundaries: Distortion increases as you move away from the central meridian. Working across zone boundaries can be inconvenient; you may need to choose a mapping projection designed for your region.
• Special zones: Some regions (notably parts of Norway and Svalbard) have special UTM zone rules in common mapping practice. A simple zone-by-longitude formula may not reflect those exceptions.
• Precision: Browser-based calculators typically round outputs. For surveying-grade work, use authoritative libraries/software and confirm parameters, units, and datum transforms.