During which battle did Horatio Nelson lose his right arm?

During the Battle of Santa Cruz de Tenerife, Rear Admiral Nelson was struck by a musket ball in the right arm, shattering his right humerus. He had gone ashore during an amphibious landing and was promptly shot. He was taken back aboard ship and most of his right arm was amputated. Within a half hour Nelson was back issuing commands.

The British were unable to achieve their goals during the battle and Nelson returned to England in order to recuperate from the injury, returning to service in March 1798.

Nelson was born in 1758 and began his naval career in 1771, signing up as a seaman, but appointed a midshipman shortly after serving aboard his first ship. He received his first command, the HMS Badger, in December 1778.

Nelson would serve during the American Revolutionary War, the French Revolutionary and Napoleonic Wars, rising to the rank of Vice-Admiral. His greatest achievement was command of the fleet during the Battle of Trafalgar in 1805, Britain's decisive naval victory over the French. The victory at Trafalgar marked the beginning of Britain's domination of the seas, held until the Second World War. But the battle also saw the end of Nelson, he was shot by a French musketeer and died shortly afterwards.