# Understanding datums and projections

A lot of technical terms are used in New Zealand’s geodetic system. Find out about geodetic and vertical datums, geoids, projections, and coordinate transformations for accurate position and height measurements.

## Geodetic datums

The positions of New Zealand’s geodetic control marks are described by coordinates on a geodetic datum.

A datum is a set of rules that lets us determine a mathematical representation of the Earth’s shape, which is described by a reference ellipsoid. This looks like a sphere that has been squashed from the top and bottom.

Reference ellipsoids

Geodetic datum coordinates are expressed as latitude (φ) and longitude (λ), with units of degrees (°), minutes (‘), and seconds (“). Heights (H) are given in metres above the surface of the ellipsoid.

Coordinate systems used in New Zealand

Since 1998 the official geodetic datum used in New Zealand and the surrounding offshore islands has been New Zealand Geodetic Datum 2000 (NZGD2000).

New Zealand Geodetic Datum 2000

## Vertical datums

The height of point is its distance above either a reference point or the surface of the vertical datum. The depth of a point is its distance below this.

Vertical datums

In the past, this reference surface was often associated with a local vertical datum or the sea surface. For sea surfaces, the reference point was established by measuring sea level at reference tide gauges over a period of time. Sea level and the size of tides will vary from place to place, so this data is difficult to combine across a region or country.

Since 2016, the official vertical datum for New Zealand region (including its offshore islands) is New Zealand Vertical Datum 2016 (NZVD2016). NZVD2016 heights are nationally consistent, repeatable and maintainable. This means we can be confident in their reliability.

New Zealand Vertical Datum 2016 (NZVD2016)

NZGD2000 heights use an ellipsoid as the reference surface, which means they are easily observed using GNSS (global navigation satellite system) techniques, such as GPS. Ellipsoid heights do not account for gravity so cannot reliability predict water flow, and cannot be used for engineering or environmental planning.

New Zealand Geodetic Datum 2000 Ellipsoidal Heights

NZGD2000 ellipsoidal and LVD heights can easily be converted to NZVD2016. For more information see: Converting between NZVD2016, NZGD2000 and local vertical datums.

## Geoids

The Earth’s gravity field varies depending on geology, the presence of mountain ranges and ocean trenches, and even water types, rainfall patterns and ice coverage.

A geoid is a lumpy, 3-dimensional model that provide a reference surface that reflects changes in gravity.

Gravity and the Geoid

Since 20016, the official geoid for New Zealand and its offshore islands is New Zealand Quasi-geoid 2016 (NZGeoid2016). This is the reference surface for NZVD2016.

## Projections

Coordinates in a geodetic datum are defined on an ellipsoid. Representing these curved geodetic coordinates on a flat surface, like a map, will cause distortion.

This can be visualised using the peel of an orange – you can only lay the peel flat if you break it. Projections let us translate curved-surface coordinates to a flat map by distorting the ellipsoid’s surface, such as stretching areas to the north and south to create a rectangular map.

Projections

Projections let us show distances in metres and kilometres, which are often more useful than degrees, minutes and seconds. However, projections always have at least a small amount of distortion so inevitably introduce some error or uncertainty.

Different types of projection exist, with most based on cylinders, cones or planes. The most common projection used in New Zealand is the transverse Mercator projection. This is based on a cylinder that lies on its side, and is aligned with a line of longitude (central meridian).

Transverse mercator transformation formulae

Since 1998, New Zealand’s official projection for topographic mapping is New Zealand Transverse Mercator 2000 (NZTM2000).

New Zealand Transverse Mercator 2000 (NZTM2000)

## Coordinate transformations

Coordinates or heights can only be used together if they use the same datum and projection. If you make calculations using a mix of datums or projections this will create errors – these can be a few metres, which you may not notice immediately, or hundreds of kilometres.

Converting coordinates between datums or projections is known as coordinate transformation. Coordinate transformations can be done using most geospatial software or tools like our online coordinate converter.