We investigate radial and vertical metallicity gradients for a sample of red clump stars from the RAdial Velocity Experiment (RAVE) Data Release 3. We select a total of 6781 stars, using a selection of colour, surface gravity and uncertainty in the derived space motion, and calculate for each star a probabilistic (kinematic) population assignment to a thin or thick disc using space motion and additionally another (dynamical) assignment using stellar vertical orbital eccentricity. We derive almost equal metallicity gradients as a function of the Galactocentric distance for the high-probability thin-disc stars and for stars with vertical orbital eccentricities consistent with being dynamically young, ev≤ 0.07, i.e. d[M/H]/dRm=−0.041 ± 0.003 and d[M/H]/dRm=−0.041 ± 0.007 dex kpc−1. Metallicity gradients as a function of the distance from the Galactic plane for the same populations are steeper, i.e. d[M/H]/dzmax=−0.109 ± 0.008 and d[M/H]/dzmax=−0.260 ± 0.031 dex kpc−1, respectively. Rm and zmax are the arithmetic mean of the perigalactic and apogalactic distances, and the maximum distance to the Galactic plane, respectively. Samples including more thick-disc red clump giant stars show systematically shallower abundance gradients. These findings can be used to distinguish between different formation scenarios of the thick and thin discs.