This paper argues that all historical data series should be accompanied by formal estimates of their margins of error. We discuss the nature of errors in data series and review earlier attempts to assess their reliability. We show how overall margins of error may be calculated for historical series from judgments on the reliability of their components, and how these allow readers both to appraise the estimate and to test the implications of applying different standards. An illustration is provided for Hoffmann’s index of British industrial output, 1770–1831. The calculations emphasize the value of this approach to the recent debate on growth rates during the industrial revolution and suggest its merits more generally.