Objectives While COVID-19 is known to be spread by respiratory droplets (which travel <2m horizontally), much less is known about its transmission via aerosols, which can become airborne and be widely distributed throughout room spaces. In order to quantify the risk posed by COVID-19 infectors exhaling respiratory aerosols in enclosed spaces, we undertook a computer modelling study to simulate transmission in an office building. Methods Respiratory droplet data from four published datasets were analysed to quantify the number and volume of droplets <100μm diameter produced by a typical cough and speaking event (i.e. counting from 1 to 100). This was used in a stochastic model to simulate (10,000 simulations) the number of respiratory particles, originating from a COVID-19 infector, that would be inhaled in one hour by a susceptible individual practicing socially distancing in a 5 x 5 x 2.75m office space. Several scenarios were simulated that mimicked the presence of both symptomatic and asymptomatic COVID-19 infectors. Results On average, each cough and speaking event produced similar numbers of droplets <100 μm diameter (median range = 955 - 1010). Computer simulations (at ventilation rate = 2AC/h) revealed that sharing the office space with a symptomatic COVID-19 infector (4 coughs per hour) for one hour resulted in the inhalation of 187.3 (median value) respiratory droplets, whereas sharing with an asymptomatic COVID-19 positive person (10 speaking events per hour) resulted in the inhalation of 482.9 droplets. Increasing the ventilation rate resulted in only modest reductions in particle numbers inhaled. Conclusions Given that live SARS-CoV-2 virions are known to be shed in high concentrations from the nasal cavity of both symptomatic and asymptomatic COVID-19 patients, the results suggest that individuals who share enclosed spaces with an infector may be at risk of contracting COVID-19 by the aerosol route, even when practicing social distancing.