Who is the leader of the senate according to the constitution?

The President of the Senate is actually the Vice President of the United States. The President Pro Tempore of Senate is the presiding officer (in the absence of the VP), which puts him or her third in the line of succession (behind the speaker of the house). The real power in the Senate, however, lies with the Senate Majority Leader and the Senate Minority Leader.

The leaders for the US Senate are the minority and majority leaders. Out of these the majority leader is considered greater.

A complex answer is required for this basic question. The President of the Senate is the Vice President of the US, who rarely presides and very rarely is even present except in a ceremonial role or when a tie vote is anticipated. The majority party really runs the Senate and it select a President pro tempore and a Majority Leader. Again, the President pro tempore rarely leads the Senate and is more of an elder statesman. The Majority Leader runs the working of the Senate and most of his or her work is done Behind the Scenes. The Majority Leader also rarely takes the seat at the front of the Senate floor, gavel in hand and managing the debate. That task is assigned to a Presiding Officer, usually a new or very junior Senator in an effort to let them learn the routine. This Senator makes very few decisions and the Parliamentarian is on hand to advise him or her. So the Senate Leader can be any of the above, but the real power is in the hands of the Majority Leader.