PurposeThis study aims to distinguish businesses by their degree of complexity and to analyse the influence of complexity on the performance of firms during the coronavirus disease 2019 (COVID-19) pandemic.Design/methodology/approachData were collected from 468 businesses, and various multivariate statistical techniques were used. Initially a factor analysis was conducted, organising variables into five factors. A discriminant analysis, performed with the five factors, allowed discriminating firms based on whether they internationalise or not. A linear regression was performed in order to estimate the contribution of each factor in the business performance.FindingsThe results suggest the existence of additional variables for measuring the complexity. From the factorial analysis it is possible to conclude that business complexity can be explained by size, indebtedness and profitability, internationalisation, number of employees, and age and leverage. Total assets, indebtedness and age are the variables that contribute the most to business performance. On the other hand, indebtedness, internationalisation, age and leverage are the independent variables that most contribute to explain business performance.Originality/valueThis paper presents advances in two ways. First, it proposes measures of complexity (highly debatable in the literature). It also proposes internationalisation as an explanation of complexity. Second, this paper sheds light on businesses decisions to grow, taking into account how complexity may affect performance.