CONDUIT4 is a Fortran code for computing the one-dimensional, steady, isothermal, multiphase and multicomponent flow of magma in volcanic conduits. The code solves the compressible mass balance and momentum balance equations separately for a gas phase and a dense phase constituted by liquid+crystals (below fragmentation), or by pyroclasts (above fragmentation). A user-defined fragmentation efficiency parameter describes the relative amounts of non-vesicular ash, vesicular pumice, and free crystals generated at fragmentation; while another user-defined parameter describes pumice degassing disequilibrium. The model takes either choked flow or atmospheric pressure conditions at the conduit exit, with the alternative being part of the solution thus depending on the selected conditions. The numerical algorithm searches for such an exit condition by adapting the mass flow-rate to the selected conduit diameter. Thermodynamic equilibrium phase between the gas (H2O+CO2) and the silicate melt is calculated through the SOLWCAD model (Papale et al., 2006, [Chemical Geology, 229(1-3), 78-95]), implemented within CONDUIT4. Magma fragmentation is determined based on Maxwell's theory for visco-elastic materials, as described in Papale (1999) [Nature, 397(6718), 425-428]. The viscosity of the liquid is calculated according to Giordano et al. (2008) [Earth and Planetary Science Letters, 271.1-4: 123-134], and the effect of crystals on viscosity is based on the model of Costa et al. (2009) [Geochemistry, Geophysics, Geosystems, 10(3)]. The transport and constitutive equations, as well as the numerical approach, are detailed in Papale (2001) [Journal of Geophysical Research: Solid Earth, 106(B6), 11043-11065].