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I am using QGIS.

Which projections / CRS are best to use for Eastern Australia (NSW in particular), which I can use to buffer points and lines in metres rather than degrees?

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For state-wide GIS data in NSW the Map projections page of NSW Spatial Services says:

GDA Lambert Projection for NSW (GDA94 Lambert, GDA2020 Lambert)

This Lambert projection is suitable for state-wide GIS data in NSW. To ensure uniformity across agencies, the Surveyor General has endorsed the following parameters for use with GDA94 and GDA2020 data.

Projection: Conformal Conic
Standard Parallels: -30º 45' 00"
-35º 45' 00"
Latitude of Origin: -33º 15' 00"
Central Meridian:   147º 00' 00"
False Easting:  9 300 000
False Northing: 4 500 000
Units:  Metre
Ellipsoid:  GRS80
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    Good choice for NSW and only little over into adjacent states based on the limited information given in the question EPSG:3308 NSW Lamberts using GDA94 datum and EPSG:8058 NSW Lamberts using GDA2020 datum... If you're going further outside the state there are EPSG:3577 GDA94 / Australian Albers and EPSG:9473 GDA2020 / Australian Albers (not fully implemented in some software yet) though the distortion is probably as bad as Google Mercator. Commented Oct 25, 2021 at 6:23

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