Understanding human cooperation is of major interest across the natural and social sciences. But it is unclear to what extent cooperation is actually a general concept. Most research on cooperation has implicitly assumed that a person's behaviour in one cooperative context is related to their behaviour in other settings, and at later times. However, there is little empirical evidence in support of this assumption. Here, we provide such evidence by collecting thousands of game decisions from over 1,400 individuals. A person's decisions in different cooperation games are correlated, as are those decisions and both self-report and real-effort measures of cooperation in non-game contexts. Equally strong correlations exist between cooperative decisions made an average of 124 days apart. Importantly, we find that cooperation is not correlated with norm-enforcing punishment or non-competitiveness. We conclude that there is a domain-general and temporally stable inclination towards paying costs to benefit others, which we dub the 'cooperative phenotype'.