Moment-based estimators of the between-study variance are very popular when performing random effects meta-analyses. This type of estimation has many advantages including computational and conceptual simplicity. Furthermore, by using these estimators in large samples, valid meta-analyses can be performed without the assumption that the treatment effects follow a normal distribution. Recently proposed moment-based confidence intervals for the between-study variance are exact under the random effects model but are quite elaborate. Here, we present a much simpler method for calculating approximate confidence intervals of this type. This method uses variance-stabilising transformations as its basis and can be used for a very wide variety of moment-based estimators in both the random effects meta-analysis and meta-regression models.