Students in my U.S. Constitutional Law course were recently perplexed by the number of different vote thresholds the Senate needs to accomplish various tasks. One student bravely asked if I would put together a list of the various thresholds. Sure, why not.
Votes need to conduct business (quorum) - a majority of seats currently filled by elected, living members.
Votes to pass a bill - a majority of members present for the vote.
Votes needed to end a filibuster (Cloture Vote) - 3/5 of the full Senate, i.e. of seats not vacant. Remember, the filibuster only exists in the Senate.
Votes needed to confirm a Presidential Appointee - majority of members present for the vote. Remember, only the Senate as confirmation power.
Votes needed to ratify a treaty - 2/3 of Senators present. Remember, only the Senate has ratification power.
Votes needed to convict and remove - 2/3 of Senators present. Remember, the House, by a simple majority, begins this process by impeaching the person.
Votes needed to override a veto - 2/3 of Senators present (House of Representatives are also needed).
Votes needed to propose an Amendment to the Constitution - 2/3 of member present. (House must also vote).