15R SiC has significant advantages over 4H and 6H SiC for certain device applications. We have measured the free exciton low temperature photoluminescence (LTPL) spectrum for E perpendicular to (c) over cap and the wavelength derivative of the absorption coefficient d alpha /d lambda, of 15R SiC for both polarizations E perpendicular to (c) over cap and E parallel to (c) over cap using modulation absorption spectroscopy. We use the E perpendicular to (c) over cap intrinsic 2 K photoluminescence spectrum to make assignments to features in the E perpendicular to (c) over cap absorption derivative spectrum. We obtain 7.15 +/-0.25 meV for the spin orbit splitting, in agreement with previous work, but with improved precision. The determination of the crystal field splitting is more challenging. We argue for a value of about SI meV. This value is in good agreement with recent calculations.