An audio fingerprint is a compact yet very robust representation of the perceptually relevant parts of an audio signal. It can be used for content-based audio identification, even when the audio is severely distorted. Audio compression changes the fingerprint slightly. We show that these small fingerprint differences due to compression can be used to estimate the signal-to-noise ratio (SNR) of the compressed audio file compared to the original. This is a useful content-based distortion estimate, when the original, uncompressed audio file is unavailable. The method uses the audio fingerprints only. For stochastic signals distorted by additive noise, an analytical expression is obtained for the average fingerprint difference as function of the SNR level. This model is based on an analysis of the Philips robust hash (PRH) algorithm. We show that for uncorrelated signals, the bit error rate (BER) is approximately inversely proportional to the square root of the SNR of the signal. This model is extended to correlated signals and music. For an experimental verification of our proposed model, we divide the field of audio fingerprinting algorithms into three categories. From each category, we select an algorithm that is representative for that category. Experiments show that the behavior predicted by the stochastic model for the PRH also holds for the two other algorithms.