Charitable giving involves a complex economic and social decision because the giver expends resources for goods or services they will never receive. Although psychologists have identified numerous factors that influence charitable giving, there currently exists no unifying computational model of charitable choice. Here, we submit one such model, based within the strictures of Psychological Value Theory (PVT). In four experiments, we assess whether charitable giving is driven by the perceived Psychological Value of the recipient. Across all four experiments, we simultaneously predict response choice and response time with high accuracy. In a fifth experiment, we show that PVT predicts charitable giving more accurately than an account based on competence and warmth. PVT accurately predicts which charity a respondent will choose to donate to and separately, whether a respondent will choose to donate at all. PVT models the cognitive processes underlying charitable donations and it provides a computational framework for integrating known influences on charitable giving. For example, we show that in-group preference influences charitable giving by changing the Psychological Values of the options, rather than by bringing about a response bias toward the in-group.