Developing a vaccine against the global pandemic SARS-CoV-2 is a critical area of active research. Modelling can be used to identify optimal vaccine dosing; maximising vaccine efficacy and safety and minimising cost. We calibrated statistical models to published dose-dependent seroconversion and adverse event data of a recombinant adenovirus type-5 (Ad5) SARS-CoV-2 vaccine given at doses 5.0 × 1010, 1.0 × 1011 and 1.5 × 1011 viral particles. We estimated the optimal dose for three objectives, finding: (A) the minimum dose that may induce herd immunity, (B) the dose that maximises immunogenicity and safety and (C) the dose that maximises immunogenicity and safety whilst minimising cost. Results suggest optimal dose [95% confidence interval] in viral particles per person was (A) 1.3 × 1011 [0.8-7.9 × 1011], (B) 1.5 × 1011 [0.3-5.0 × 1011] and (C) 1.1 × 1011 [0.2-1.5 × 1011]. Optimal dose exceeded 5.0 × 1010 viral particles only if the cost of delivery exceeded £0.65 or cost per 1011 viral particles was less than £6.23. Optimal dose may differ depending on the objectives of developers and policy-makers, but further research is required to improve the accuracy of optimal-dose estimates.