We present the first experimental method to non-parametrically elicit utility functions and associated measures of (higher order) risk preferences. The method yields well-known theoretically-derived utility-based measures of intensities, such as the Arrow-Pratt measure for risk aversion, and analogous measures for prudence and temperance. Unlike parametric alternatives, the method is free of assumptions about the shape of the utility function, and particularly of the commonly made but provenly inappropriate ones for the study of higher order risk preferences. The method’s ability to account for decision errors is illustrated in a simulation exercise, where it performs comparable to parametric fitting techniques. In accompanying laboratory and online experiments, we validate our method and find significant relations to other methods. Finally, we apply our method in a sample of the poor population in Bogotá, Colombia to test the precautionary saving model by Leland (1968). We find strong support for the model by showing that income risk is associated with increases in savings for prudent individuals.