UTM Scale Factor Calculator
Compute the precise ellipsoidal UTM point scale factor and grid convergence from latitude and longitude (WGS84), or a quick approximation from an easting.
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How to use this calculator
- Precise mode (the default): enter the latitude and longitude. Leave the zone blank for the standard zone, or enter one to work in a neighbouring zone.
- Quick approximation: choose it from Mode and enter just the easting (and, optionally, the sphere radius).
- Press Calculate and read the point scale factor — plus, in precise mode, the grid convergence, zone, easting and northing.
How it works
Precise mode computes the ellipsoidal point scale factor on WGS84 with Krüger's series to sixth order, in the form published by Charles Karney (2011). It was checked against GeographicLib on 45 positions across both hemispheres, 13 zones and up to 6° from the central meridian, agreeing to within about one part in 100 billion.
The quick approximation uses k ≈ k₀·(1 + E′²/(2R²)), where E′ is the easting minus the 500,000 m false easting and k₀ = 0.9996. An easting alone cannot give the ellipsoidal factor, so this mode is labelled as an approximation.
Worked example
Perth: 31.95° S, 115.86° E. Zone 50, about 108 km west of the central meridian (117° E): the precise scale factor is about 0.99974, so grid distances there are roughly 260 mm per kilometre shorter than on the ellipsoid.
Frequently asked questions
Why is it less than 1 near the central meridian?
UTM uses k₀ = 0.9996 so the projection is slightly compressed at the central meridian and slightly stretched at the zone edges, balancing distortion.
How accurate is the precise mode?
It agrees with GeographicLib — the reference implementation by Charles Karney — to within about 1 × 10⁻¹¹ on 45 test positions, ten times inside the 1 × 10⁻¹⁰ target. It covers 80° S to 84° N and up to 6° either side of the zone's central meridian, and refuses positions outside that rather than guessing.
What is grid convergence?
The angle between true north and grid north at the point. It is zero on the central meridian and grows towards the zone edges; it is positive east of the central meridian in the northern hemisphere.
Related tools
- Combined Scale Factor Helper
- Easting/Northing Distance Calculator
- Antenna Height Slant to Vertical Converter
- Grid Convergence Angle Calculator
- Lat/Long to UTM Converter (WGS84)
- MGA94 to MGA2020 Coordinate Converter
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Cite this tool
Zerdly. (2026). UTM Scale Factor Calculator. Retrieved from https://www.zerdly.com/tools/utm-scale-factor-calculator/
Tip: Enter any known values to calculate the remaining results.
Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.