Results of constant‐pressure Monte Carlo calculations on dense fluid nitrogen over a pressure range of 2 to 300 kbar and a temperature range of 300–3000 K are presented. From analytic fits to the calculated volumes, enthalpies and vibrational frequency shifts, a comprehensive set of thermodynamic quantities is derived, including: thermal expansivity, compressibility, specific heat, Grüneisen parameter, and speed of sound. Comparison of the theoretical results to experiment at room temperature shows very good agreement (within 0.3% in volume and 1% in speed of sound, for instance). Good agreement is also obtained with earlier simulation data. In agreement with experimental studies of fluid metals, we find that the speed of sound varies linearly with density; along isotherms as well as along the Hugoniot. We find that ργ G , the density times the Grüneisen parameter, which is assumed to be a constant in an often‐used phenomenological equation of state, varies considerably with density and temperature. Comparison is made with results from a ‘‘soft sphere’’ model presented in an accompanying paper.