Utilities · Conversions & survey
Coordinates: MGA2020 ↔ latitude / longitude calculator
Converts geographic coordinates (latitude, longitude on GDA2020) to Map Grid of Australia easting and northing in the correct zone, and back, using the Krüger series to sixth order (as in the ICSM GDA2020 Technical Manual). Also gives the grid convergence and degrees–minutes–seconds.
Standard: GDA2020 / MGA2020 transverse Mercator (k0 = 0.9996, false E 500 000, false N 10 000 000) on GRS80 · Krüger n-series to n⁶ (Karney 2011), sub-millimetre
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Conversion | Latitude/longitude → MGA | |
| Latitude (negative south) | -27.4698 | ° |
| Longitude | 153.0251 | ° |
| Easting | 502479.869 | m |
| Northing | 6961528.093 | m |
| MGA zone (0 = from longitude) | 0 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| MGA zone | 56 | |
| Easting | 502,479.869 | m |
| Northing | 6,961,528.093 | m |
| Latitude | -27.469800000° (−27° 28′ 11.2800″) | |
| Longitude | 153.025100000° (153° 1′ 30.3600″) | |
| Grid convergence | -0.011578 | ° |
- ✓ Point within the zone (±3° of the central meridian)
- ✓ Southern hemisphere (MGA false northing)
Method, formulas and assumptions
- Forward: t = sinh(atanh(sinφ) − e·atanh(e·sinφ)), ξ′ = atan(t/cosΔλ), η′ = atanh(sinΔλ/√(1 + t²)); ξ = ξ′ + Σαj·sin2jξ′·cosh2jη′, η = η′ + Σαj·cos2jξ′·sinh2jη′; E = 500 000 + k0Aη, N = 10 000 000 + k0Aξ.
- Inverse with the βj series and Newton iteration for the conformal latitude.
- GRS80: a = 6 378 137 m, 1/f = 298.257222101. Check: Flinders Peak (GDA2020 TM example) converts to E 273 741.297, N 5 796 489.777 in zone 55.
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