If you are moving at 1/4 impulse or greater or at full reverse, then your turn rate is approximately

turn_rate = base_turn_rate + (base_turn_rate - 3) * (0.38 * impulse_thrusters_skill / 99 + engine_power / 100 + bonus_from_consoles + bonus_from_engines).

I'm reasonably sure the above formula is accurate, though I haven't tested turn rates in a while. The factor of 0.38 modifying impulse thrusters skill might be a little off. The above formula doesn't include boff abilities; I would also be interested in knowing how they fit into this.

Skills and bonuses also affect the turn rate at full stop, but because the effect is so small, I cannot infer what the exact formula is.