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SHTOOLS LOGO Documentation DOI Paper Binder Chat on matrix Chat at gitter License Mastodon Follow

SHTOOLS/pyshtools is a Fortran-95/Python library that can be used for spherical harmonic transforms, multitaper spectral analyses, expansions of gridded data into Slepian basis functions, standard operations on global gravitational and magnetic field data.



  • Supports all standard normalizations and phase conventions of the spherical harmonic functions.

  • Effortless conversion between real and complex harmonics, and between different normalization and phase conventions.

  • Use of both regularly sampled geographic grids and grids appropriate for Gauss-Legendre quadrature.

  • Spherical harmonic transforms proven to be accurate up to about degree 2800 for the native Fortran 95 backend and beyond using the DUCC0 backend.

  • Perform localized multitaper spectral analyses, or expand gridded data in terms of localized Slepian basis functions.

  • Support for standard data and file formats, including xarray and netcdf.

  • Import research-grade gravity, topography, and magnetic field datasets with a single command.

  • Creation of publication quality maps using Cartopy and PyGMT.

  • Support multithreaded programming using the OpenMP API.


A variety of Python tutorials and guides are available to explain the main library features. To get started, click on the following Python tutorials and run them interactively in Binder:


SHTOOLS can be invoked in any Fortran 95 or Python program. The core software is written in Fortran 95, and Python wrappers and dedicated classes allow simple access to the fortran-compiled routines. To install it, run these commands below:

pyshtools (for Python)

Install using conda:
conda install -c conda-forge pyshtools  # Linux and macOS only
conda update -c conda-forge pyshtools  # to upgrade a pre-existing installation
Install using pip:
pip install pyshtools
pip install --upgrade pyshtools  # to upgrade a pre-existing installation
pip install pyshtools --no-binary pyshtools  # build from source
pip install git+  # install the develop branch from source
For developers:

Install the requirements:

# Linux: install gfortran, fftw3, blas, and lapack
sudo apt-get install g++ gfortran libfftw3-dev libblas-dev liblapack-dev
# macOS: install fftw using brew or macports
brew install fftw
sudo port install fftw-3
# macOS: for LAPACK, link to the system '-framework Accelerate' or install openblas

Then clone the shtools repo and install manually:

git clone
cd shtools
git checkout develop
pip install -e .  # install into the shtools folder and link to the active python environment

SHTOOLS (for Fortran 95)

Install using the brew package manager (MacOS, Linux, Windows):
brew install shtools
Install using the macports package manager (MacOS):
sudo port install shtools
Install from source:

Clone or download the this repo, and then execute one (or both) of the following commands in the shtools directory:

make fortran
make fortran-mp  # for OpenMP Fortran routines

Further installation instructions and options can be found in the web documentation.


We work on the develop branch and only push releases to master. Please base all pull requests on develop.


For the full list of contributors, see the AUTHORS file.


This project uses the BSD 3-Clause license, as found in the LICENSE file.


  • Mark A. Wieczorek and Matthias Meschede (2018). SHTools --- Tools for working with spherical harmonics, Geochemistry, Geophysics, Geosystems, 19, 2574-2592, doi:10.1029/2018GC007529.
  • Mark Wieczorek, et al. (2019). SHTOOLS/SHTOOLS. Zenodo, doi:10.5281/zenodo.3457861