The pseudorapidity density of charged particles, dN(ch)/d eta, in p-Pb collisions has been measured at a centre of-mass energy per nucleon-nucleon pair of root S-NN =3D 8.16 TeV at mid-pseudorapidity for non-single-diffractive events. The results cover 3.6 units of pseudorapidity, vertical bar eta vertical bar < 1.8. The dN(ch)/d eta value is 19.1 +/- 0.7 at vertical bar eta vertical bar < 0.5. This quantity divided by < N-part >/2 is 4.73 +/- 0.20, where < N-part > is the average number of participating nucleons, is 9.5% higher than the corresponding value for p-Pb collisions at root S-NN =3D 5.02 TeV. Measurements are compared with models based on different mechanisms for particle production. All models agree within uncertainties with data in the Pb-going side, while HIJING overestimates, showing a symmetric behaviour, and EPOS underestimates the p-going side of the dN(ch)/d eta distribution. Saturation-based models reproduce the distributions well for eta > -1.3. The dN(ch)/d eta is also measured for different centrality estimators, based both on the charged particle multiplicity and on the energy deposited in the Zero Degree Calorimeters. A study of the implications of the large multiplicity fluctuations due to the small number of participants for systems like p-Pb in the centrality calculation for multiplicity-based estimators is discussed, demonstrating the advantages of determining the centrality with energy deposited near beam rapidity.
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