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Stealth Rock is placed on the opponent's field and damages any Pokémon when they switch in. The base damage is 12.5%, and is affected by the target's susceptibility to Rock; Pokémon that are 4x weak to Rock will receive 50% max HP damage; 2x weak to Rock will result in 25%; a 2x resist will take 6.25%, and any Pokémon with a 4x resistance to Rock will only receive 3.125% max HP damage. This lasts until the opponent uses Rapid Spin.
Smogon has an article on this topic.