Uncertainty of decibel levels

The mean sound exposure level from a source is routinely estimated by the mean of the observed sound exposures from repeated measurements. A formula for the standard uncertainty based on the Guide to the expression of Uncertainty in Measurement (GUM) is derived. An alternative formula is derived for the case where the GUM method fails. The formulas are applied on several examples, and compared with a Monte Carlo calculation of the standard uncertainty. The recommended formula can be seen simply as a convenient translation of the uncertainty on an energy scale into the decibel level scale, but with a theoretical foundation.