For measuring the root-mean-square value, a circuit is specified which operates in accordance with the principles of stochastic mathematics and by means of which the root-mean-square value can be measured within a greater frequency range and with a simpler circuit than in the known method. In this arrangement, the voltage to be measured is directly supplied to the input of a comparator which is thus the switching element which determines the upper cut-off frequency. The root-mean-square value is calculated in a subsequent microcomputer, the arithmetic operations of which relate to counting results which are obtained by sampling at the comparator output.