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• Access to physical items (e.g. brush, teat) improved growth; pair housing did not. • Physical items reduced undesirable behaviours (e.g. non-nutritive sucking). • Social housing promoted positive behaviours (e.g. locomotor play and sniffing). • The combination of physical items and social housing showed no further improvement. • The treatments had no effect on calf fear in novel environment and object tests. The objective of this study was to determine the effects of social housing, the provision of physical enrichment, and the interaction between the two on calf growth, behaviour and fearfulness. Forty-eight calves were randomly allocated to either individual (IP, sixteen calves) or pair (PP, thirty-two calves) pens from 2 days to 8 weeks of age. Half of the calves in each housing treatment were provided with physical enrichment items (stationary brushes, plastic chains, rubber teats and haynets filled with strawberry-scented hay; PE). The remaining calves received no physical enrichment items (NPE). Concentrate consumption within each pen was measured daily and calves were weighed at birth and weekly thereafter. Concentrate feeding efficiency was then calculated by the ratio between average daily gain within each pen and daily concentrate consumption within each pen. When calves were 2–5 weeks of age, they were recorded by a camera between 06:00 h and 20:00 h twice weekly, and behavioural data were collected using instantaneous scan sampling at 5-min intervals. Their behavioural responses to a novel environment and a novel object were then assessed once each at 5 or 6 weeks of age. PE calves tended to have greater average daily gains than NPE calves (mean ± IQR; 610.6 ± 151.8 g/d vs. 568.8 ± 77.1 g/d; p = 0.095). PE calves spent more time consuming hay than NPE calves. Among calves in IP pens, PE calves consumed less concentrate but had better concentrate feeding efficiency than NPE calves. For home pen behaviours, PE calves showed less frequent non-nutritive sucking than NPE calves (0.802 ± 0.451 % vs. 1.897 ± 0.401 % of scans) and less frequent cross-sucking. Furthermore, PP increased or tended to increase the time spent on locomotor play, fixture sniffing, social sniffing, allogrooming and cross-sucking, but tended to decrease non-nutritive sucking compared to IP. No treatment effects were found on behaviour in the novelty tests. In conclusion, physical enrichment may improve calf growth more effectively than social housing does. Physical enrichment and social housing may satisfy diverse natural behaviours and reduce undesirable behaviour in different ways. However, these treatments had no effect on calf fear responses in novel environment and object tests. The combination of physical enrichment and social housing showed no further improvement in calf welfare. [ABSTRACT FROM AUTHOR]