We describe an extension to the SOFTSUSY program that provides for the calculation of the sparticle spectrum in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), where a chiral superfield that is a singlet of the Standard Model gauge group is added to the Minimal Supersymmetric Standard Model (MSSM) fields. Often, a ℤ3 symmetry is imposed upon the model. SOFTSUSY can calculate the spectrum in this case as well as the case where general ℤ3 violating (denoted as ℤ3) terms are added to the soft supersymmetry breaking terms and the superpotential. The user provides a theoretical boundary condition for the couplings and mass terms of the singlet. Radiative electroweak symmetry breaking data along with electroweak and CKM matrix data are used as weak-scale boundary conditions. The renormalisation group equations are solved numerically between the weak scale and a high energy scale using a nested iterative algorithm. This paper serves as a manual to the NMSSM mode of the program, detailing the approximations and conventions used. Program Summary Program title: SOFTSUSY Catalogue identifier: ADPM-v4-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPM-v4-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/ licence/licence.html No. of lines in distributed program, including test data, etc.: 154886 No. of bytes in distributed program, including test data, etc.: 1870890 Distribution format: tar.gz Programming language: C++, fortran. Computer: Personal computer. Operating system: Tested on Linux 3.x. Word size: 64 bits Classification: 11.1, 11.6. Does the new version supersede the previous version?: Yes Catalogue identifier of previous version: ADPM-v3-0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 785 Nature of problem: Calculating supersymmetric particle spectrum and mixing parameters in the next-to-minimal supersymmetric standard model. The solution to the renormalisation group equations must be consistent with boundary conditions on supersymmetry breaking parameters, as well as on the weak-scale boundary condition on gauge couplings, Yukawa couplings and the Higgs potential parameters. Solution method: Nested iterative algorithm and numerical minimisation of the Higgs potential. Reasons for new version: Major extension to include the next-to-minimal supersymmetric standard model. Summary of revisions: Added additional supersymmetric and supersymmetry breaking parameters associated with the additional gauge singlet. Electroweak symmetry breaking conditions are significantly changed in the next-to-minimal mode, and some sparticle mixing changes. An interface to NMSSMTools has also been included. Some of the object structure has also changed, and the command line interface has been made more user friendly. Restrictions: SOFTSUSY will provide a solution only in the perturbative regime and it assumes that all couplings of the model are real (i.e. CP-conserving). If the parameter point under investigation is non-physical for some reason (for example because the electroweak potential does not have an acceptable minimum), SOFTSUSY returns an error message. Running time: A few seconds per parameter point.