A wellbore fluid pressure measurement system includes a densometer adapted to measure a fluid density of a fluid flowing in a tubing system; and a monitoring unit communicably coupled to the densometer. The monitoring unit is adapted to receive a plurality of values representative of the fluid density from the densometer and includes a memory adapted to store the plurality of values representative of the fluid density; and one or more processors operable to execute a fluid pressure measurement module. The module is operable when executed to determine a fluid pressure of the fluid based on at least a portion of the values representative of the fluid density.