Approximate adders have been considered as a potential alternative for error-tolerant applications to trade off some accuracy for gains in other circuit-based metrics, such as power, area and delay. Existing approximate adder designs have shown substantial advantages in improving many of these operational features. However, the error characteristics of the approximate adders still remain an issue that is not very well understood. A simulation-based method requires both programming efforts and a time-consuming execution for evaluating the effect of errors. This method becomes particularly expensive when dealing with various sizes and types of approximate adders. In this paper, a framework based on analytical models is proposed for evaluating the error characteristics of approximate adders. Error features such as the error rate and the mean error distance are obtained using this framework without developing functional models of the approximate adders for time-consuming simulation. As an example, the estimate of peak signal-to-noise ratios (PSNRs) in image processing is considered to show the potential application of the proposed analysis. This analytical framework provides an efficient method to evaluate various designs of approximate adders for meeting different figures of merit in error-tolerant applications.