Data consistency conditions (DCC) are mathematical equations characterizing the redundancy in X-ray projections. They have been successfully used to calibrate the scanner geometry or correct projections (e.g. for beam hardening or scatter). Evaluating the DCC implies the computation of moments of the projections. Since the projections are subject to random noise, DCC will be as well. Accounting for this uncertainty would likely improve DCC-based algorithms which estimate some model parameters by maximizing the consistency between projections. In this work, we calculate the variance of DCC assuming known and uncorrelated noise in the projection pixels, following the approach used to compute noise in computed tomography (CT) images reconstructed with a filtered-backprojection algorithm. The DCC are computed between pairs of cone-beam projections acquired on a helical trajectory. The variance formula was validated with batch simulations. Large noise differences were observed in this set of DCC, up to two orders of magnitude, which demonstrates that it is crucial to account for this noise in DCC-based algorithms.