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Bedrock river profiles are often interpreted with the aid of slope–area analysis, but noisy topographic data make such interpretations challenging. We present an alternative approach based on an integration of the steady‐state form of the stream power equation. The main component of this approach is a transformation of the horizontal coordinate that converts a steady‐state river profile into a straight line with a slope that is simply related to the ratio of the uplift rate to the erodibility. The transformed profiles, called chi plots, have other useful properties, including co‐linearity of steady‐state tributaries with their main stem and the ease of identifying transient erosional signals. We illustrate these applications with analyses of river profiles extracted from digital topographic datasets. Copyright © 2012 John Wiley & Sons, Ltd.