We propose a measure of the degree of ambiguity associated with a belief function and a nonparametric method to estimate it. The degree of ambiguity associated with a belief function is measured by the Kullback-Leibler diameter of the set of probability measures compatible with it. It is shown that an estimator based on the empirical version of the unambiguous measure generating the belief function is consistent for the true value of the ambiguity measure. Applications to policy decision making under Knightian uncertainty are discussed.