I argue that both Hobbes and Spinoza rely on a pivot epicurean idea to form their conceptions of the social contract, namely, the idea that the human acts by calculating their utility. However, Hobbes and Spinoza employ this starting principle in different ways. For Hobbes, this only makes sense if the calculation of utility is regulated by fear as the primary political emotion. For Spinoza, there is no primary emotion and the entire construction of the social contract relies on how the calculation of utility is carried out. I argue that this conception of the social contract leads Spinoza to espouse a radical position about the political, which has been overlooked by those like Antonio Negri who read Spinoza as a radical democrat.