Distances to individual stars in our own Galaxy are critical in order to piece together the nature of its velocity and spatial structure. Core helium burning red clump (RC) stars have similar luminosities, are abundant throughout the Galaxy and thus constitute good standard candles. We build a hierarchical probabilistic model to quantify the quality of RC stars as standard candles using parallax measurements from the first Gaia data release. A unique aspect of our methodology is to fully account for (and marginalize over) parallax, photometry and dust correction uncertainties, which lead to more robust results than standard approaches. We determine the absolute magnitude and intrinsic dispersion of the RC in 2MASS bands J, H, Ks, GaiaG band and WISE bands W1, W2, W3 and W4. We find that the absolute magnitude of the RC is −1.61 ± 0.01 (in Ks), +0.44 ± 0.01 (in G), −0.93 ± 0.01 (in J), −1.46 ± 0.01 (in H), −1.68 ± 0.02 (in W1), −1.69 ± 0.02 (in W2), −1.67 ± 0.02 (in W3) and −1.76 ± 0.01 mag (in W4). The mean intrinsic dispersion is ∼0.17 ± 0.03 mag across all bands (yielding a typical distance precision of ∼8 per cent). Thus RC stars are reliable and precise standard candles. In addition, we have also re-calibrated the zero-point of the absolute magnitude of the RC in each band, which provides a benchmark for future studies to estimate distances to RC stars. Finally, the parallax error shrinkage in the hierarchical model outlined in this work can be used to obtain more precise parallaxes than Gaia for the most distant RC stars across the Galaxy.