Research in animals suggests that decisions about physical versus cognitive effort have distinct neural bases, but exploration of this question in humans is hampered by lack of parallel measures of physical and cognitive effort for rewards. We developed a novel measure of willingness to exert cognitive effort for rewards, the C-EEfRT, paralleling the validated physical effort expenditure for rewards task (EEfRT). To validate the C-EEfRT we: (a) tested whether EEfRT and C-EEfRT tasks were equivalently difficult; (b) tested whether decisions on the EEfRT and C-EEfRT were equivalently responsive to changes in reward; (c) examined relationships between the C-EEfRT and anhedonia, intelligence, and working memory. Last, we tested the relationship between willingness to exert physical and cognitive effort for rewards in humans. Sixty healthy adults completed the EEfRT, the C-EEfRT, an anhedonia self-report, an intelligence test, and a working memory task. Overall willingness to exert effort was higher on the C-EEfRT than the EEfRT, particularly when reward probability and amount were low. This was despite participants perceiving the cognitive task as more difficult, and having greater difficulty completing it. Differential effects of physical fatigue may have contributed. Anhedonia was not related to effort on either measure. Working memory, but not intelligence, was associated with cognitive effort. There was a moderate relationship between cognitive and physical effort. These findings suggest the importance of measuring cognitive effort as distinct from physical effort in humans. Future studies should consider calibrating task difficulty for each individual, and exploring cognitive effort in clinical populations.