Stray neutron exposures pose a potential risk for the development of secondary cancer in patients receiving proton therapy. However, the behavior of the ambient dose equivalent is not fully understood, including dependences on neutron spectral fluence, radiation weighting factor and proton treatment beam characteristics. The objective of this work, therefore, was to estimate neutron exposures resulting from the use of a passively scattered proton treatment unit. In particular, we studied the characteristics of the neutron spectral fluence, radiation weighting factor and ambient dose equivalent with Monte Carlo simulations. The neutron spectral fluence contained two pronounced peaks, one a low-energy peak with a mode around 1 MeV and one a high-energy peak that ranged from about 10 MeV up to the proton energy. The mean radiation weighting factors varied only slightly, from 8.8 to 10.3, with proton energy and location for a closed-aperture configuration. For unmodulated proton beams stopped in a closed aperture, the ambient dose equivalent from neutrons per therapeutic absorbed dose (H*(10)/D) calculated free-in-air ranged from about 0.3 mSv/Gy for a small scattered field of 100 MeV proton energy to 19 mSv/Gy for a large scattered field of 250 MeV proton energy, revealing strong dependences on proton energy and field size. Comparisons of in-air calculations with in-phantom calculations indicated that the in-air method yielded a conservative estimation of stray neutron radiation exposure for a prostate cancer patient.