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Fast lon, lat to and from ETRS89 and BNG (OSGB36) using the OS OSTN15 transform via Rust FFI

Project description

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A utility library for converting decimal WGS84 longitude and latitude coordinates into ETRS89 (EPSG:25830) and/or British National Grid (More correctly: OSGB36, or EPSG:27700) Eastings and Northings, and vice versa.

Conversion is handled by a Rust binary using FFI, and is quite fast. Some benchmarks can be found here.


pip install convertbng
Please use an up-to-date version of pip (8.1.2 as of June 2016)

Supported Platforms

The package has been built for and tested on the following platforms:

  • Linux x86_64 and aarch64 Python 3.{7, 8, 9, 10, 11} (Manylinux2014)
  • macOS x86_64 and arm64 Python 3.{7, 8, 9, 10, 11}
  • Windows 64-bit Python 3.{7, 8, 9, 10, 11}

Windows Binaries

The Rust DLL and the Cython extension used by this package have been built with an MSVC toolchain. You shouldn't need to install any additional runtimes in order for the wheel to work, but please open an issue if you encounter any errors.


The functions accept either a sequence (such as a list or numpy array) of longitude or easting values and a sequence of latitude or northing values, or a single longitude/easting value and single latitude/northing value. Note the return type:
"returns a list of two lists containing floats, respectively"

NOTE: Coordinate pairs outside the BNG bounding box, or without OSTN15 coverage will return a result of
[[nan], [nan]], which cannot be mapped. Since transformed coordinates are guaranteed to be returned in the same order as the input, it is trivial to check for this value. Alternatively, ensure your data fall within the bounding box before transforming them:

East: 1.7800
West: -7.5600
North: 60.8400
South: 49.9600

All functions try to be liberal about what containers they accept: list, tuple, array.array, numpy.ndarray, and pretty much anything that has the __iter__ attribute should work, including generators.

from convertbng.util import convert_bng, convert_lonlat

# convert a single value
res = convert_bng(lon, lat)

# convert longitude and latitude to OSGB36 Eastings and Northings using OSTN15 corrections
lons = [lon1, lon2, lon3]
lats = [lat1, lat2, lat3]
res_list = convert_bng(lons, lats)

# convert lists of BNG Eastings and Northings to longitude, latitude
eastings = [easting1, easting2, easting3]
northings = [northing1, northing2, northing3]
res_list_en = convert_lonlat(eastings, northings)

# assumes numpy imported as np
lons_np = np.array(lons)
lats_np = np.array(lats)
    res_list_np = convert_bng(lons_np, lats_np)

Cython Module

If you're comfortable with restricting yourself to NumPy f64 arrays, you may use the Cython functions instead. These are identical to those listed below, but performance on large datasets is better. They are selected by changing the import statement
from convertbng.util import to
from convertbng.cutil import

The conversion functions will accept most sequences which implement __iter__, as above (list, tuple, float, array.array, numpy.ndarray), but will always return NumPy f64 ndarray. In addition, you must ensure that your inputs are float, f64, or d in the case of array.array.

But I Have a List of Coordinate Pairs

coords = [[1.0, 2.0], [3.0, 4.0]]
a, b = list(zip(*coords))
# a is (1.0, 3.0)
# b is (2.0, 4.0)

But I have Shapely Geometries

from convertbng.util import convert_etrs89_to_ll
from shapely.geometry import LineString
from shapely.ops import transform
from math import isnan
from functools import partial

def transform_protect_nan(f, xs, ys):
    # This function protects Shapely against NaN values in the output of the
    # transform, which would otherwise case a segfault.
    xs_t, ys_t = f(xs, ys)
    assert not any([isnan(x) for x in xs_t]), "Transformed xs contains NaNs"
    assert not any([isnan(y) for y in ys_t]), "Transformed ys contains NaNs"
    return xs_t, ys_t

convert_etrs89_to_lonlat_protect_nan = partial(transform_protect_nan, convert_etrs89_to_ll)

line = LineString([[651307.003, 313255.686], [651307.004, 313255.687]])

new_line = transform(convert_etrs89_to_lonlat_protect_nan, line)

Available Conversions (AKA I Want To…)

  • transform longitudes and latitudes to OSGB36 Eastings and Northings very accurately:
    • use convert_bng()
  • transform OSGB36 Eastings and Northings to longitude and latitude, very accurately:
    • use convert_lonlat()
  • transform longitudes and latitudes to ETRS89 Eastings and Northings, very quickly (without OSTN15 corrections):
    • use convert_to_etrs89()
  • transform ETRS89 Eastings and Northings to ETRS89 longitude and latitude, very quickly (the transformation does not use OSTN15):
    • use convert_etrs89_to_lonlat()
  • convert ETRS89 Eastings and Northings to their most accurate real-world representation, using the OSTN15 corrections:
    • use convert_etrs89_to_osgb36()

Provided for completeness:

  • transform accurate OSGB36 Eastings and Northings to less-accurate ETRS89 Eastings and Northings:
    • use convert_osgb36_to_etrs89()

Relationship between ETRS89 and WGS84

From Transformations and OSGM02™ User guide, p7. Emphasis mine.

[…] ETRS89 is a precise version of the better known WGS84 reference system optimised for use in Europe; however, for most purposes it can be considered equivalent to WGS84. Specifically, the motion of the European continental plate is not apparent in ETRS89, which allows a fixed relationship to be established between this system and Ordnance Survey mapping coordinate systems. Additional precise versions of WGS84 are currently in use, notably ITRS; these are not equivalent to ETRS89. The difference between ITRS and ETRS89 is in the order of 0.25 m (in 1999), and growing by 0.025 m per year in UK and Ireland. This effect is only relevant in international scientific applications. For all navigation, mapping, GIS, and engineering applications within the tectonically stable parts of Europe (including UK and Ireland), the term ETRS89 should be taken as synonymous with WGS84.

In essence, this means that anywhere you see ETRS89 in this README, you can substitute WGS84.

What CRS Are My Data In

  • if you have latitude and longitude coordinates:
    • They're probably WGS84. Everything's fine!
  • if you got your coordinates from a smartphone or a consumer GPS:
    • They're probably WGS84. Everything's fine!
  • if you have x and y coordinates, or you got your coordinates from Google Maps or Bing Maps and they look something like (-626172.1357121646, 6887893.4928337997), or the phrase "Spherical Mercator" is mentioned anywhere:
    • they're probably in Web Mercator. You must convert them to WGS84 first. Use convert_epsg3857_to_wgs84([x_coordinates], [y_coordinates]) to do so.


convert_bng and convert_lonlat first use the standard seven-step Helmert transform to convert coordinates. This is fast, but not particularly accurate – it can introduce positional error up to approximately 5 metres. For most applications, this is not of particular concern – the input data (especially those originating with smartphone GPS) probably exceed this level of error in any case. In order to adjust for this, the OSTN15 adjustments for the kilometer-grid the ETRS89 point falls in are retrieved, and a linear interpolation to give final, accurate coordinates is carried out. This process happens in reverse for convert_lonlat.


OSTN15 data are used for highly accurate conversions from ETRS89 latitude and longitude, or ETRS89 Eastings and Northings to OSGB36 Eastings and Northings, and vice versa. These data will usually have been recorded using the National GPS Network:

Accuracy of Your Data

Conversion of your coordinates using OSTN15 transformations will be accurate, but if you're using consumer equipment, or got your data off the web, be aware that you're converting coordinates which probably weren't accurately recorded in the first place. That's because accurate surveying is difficult.

Accuracy of the OSTN15 transformation used in this library

  • ETRS89 longitude and latitude / Eastings and Northings to OSGB36 conversion agrees with the provided Ordnance Survey test data in 39 of the 40 test coordinates (excluding two coordinates designed to return no data; these correctly fail).
  • The only discrepancy – in point TP31– is 1mm.
  • OSGB36 to ETRS89 longitude and latitude conversion is accurate to within 8 decimal places, or 1.1mm.

A Note on Ellipsoids

WGS84 and ETRS89 coordinates use the GRS80 ellipsoid, whereas OSGB36 uses the Airy 1830 ellipsoid, which provides a regional best fit for Britain. Positions for coordinates in Great Britain can differ by over 100m as a result. It is thus inadvisable to attempt calculations using mixed ETRS89 and OSGB36 coordinates.



The main detail of interest is the FFI interface between Python and Rust, the Python side of which can be found in (the ctypes implementation), cutil.pyx (the cython implementation), and the Rust side of which can be found in
The ctypes library expects C-compatible data structures, which we define in Rust (see above). We then define methods which allow us to receive, safely access, return, and free data across the FFI boundary.
Finally, we link the Rust conversion functions from again. Note the errcheck assignments, which convert the FFI-compatible ctypes data structures to tuple lists.

Building the binary for local development

  • ensure you have Rust 1.x and Cargo installed
  • download the Rust extension for your platform from github
  • copy the binary into the convertbng directory
  • run python build_ext --inplace


  • install pytest
  • run pytest



Citing Convertbng

If Convertbng has been significant in your research, and you would like to acknowledge the project in your academic publication, we suggest citing it as follows (example in APA style, 7th edition):

Hügel, S. (2021). Convertbng (Version X.Y.Z) [Computer software].

In Bibtex format:

author = {Hügel, Stephan},
doi = {10.5281/zenodo.5774931},
license = {MIT},
month = {12},
title = {{Convertbng}},
url = {},
version = {X.Y.Z},
year = {2021}

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