A method for determining the gas pressure may include generating, via a downhole tool, neutron radiation in a cased wellbore of a geological formation and measuring a response to the neutron radiation. The method may also include determining, via a processor, at least one of a sigma, a neutron porosity, or a fast-neutron cross-section of the formation. Additionally, an equation of state of the gas may be estimated, and a gas pressure of the gas may be determined by solving a relationship, based at least in part on the equation of state, between the gas pressure and the at least one of the sigma, the neutron porosity, or the fast-neutron cross-section.