Most theoretical work on how to calculate the marginal deadweight loss has been done for linear taxes and for variations in linear budget constraints. This is quite surprising because most income tax systems are nonlinear, generating nonlinear budget constraints. Instead of developing the proper procedure to calculate the marginal deadweight loss for variations in nonlinear income taxes, a common procedure has been to linearize the nonlinear budget constraint and apply methods that are correct for variations in a linear income tax. Such a procedure leads to incorrect results. The main purpose of this paper is to show how to correctly calculate the marginal deadweight loss when the income tax is nonlinear. A second purpose is to evaluate the bias in results that obtains when a linearization procedure is used. Our main theoretical result is that the overall curvature of the tax system plays the same role as the curvature of indifference curves for the size of the marginal deadweight loss. Using numerical simulations calibrated on US data, we show that common linearization procedures may lead to substantial overestimation of the marginal deadweight loss.