I have lived in my home for 2 years. I signed a 1 year lease when I first moved in. I did not sign a new lease.I did not sign a month to month lease. I am moving on yhe 13th of this month. He is saying I owe for a whole month. Do I pay a whole month or a half of months rent legally.

You LEGALLY have to pay a FULL months rent... and you HAVE to give 30 days advance notice. A rental month is considered the First of the month to the last day of that month.

A month to month lease is legally implied... you don't sign that. It's the default condition in absence of a longer written lease. You should check your old lease and make sure there is not a clause where it automatically renews for a second year absent any written notice you intend to leave. Most don't have that, I've seen a few that do. Those tended to be apartments.

Yes. You pay by the month. Not the week, day or year. The landlord is not obligated to pro-rate your last months rent.

The entire month, in fact you would have had to give them a full month notice. At the first of this month and owe the entire month.

Also, note, even when the lease expired, the terms of that lease turn into your month to month rental, so if it states 60 days, actually he can require that. It is the lease terms that decide how he returns your deposit and so on.

The lease expire only ends the date of rental, and allows him to raise rents.

Be happy that he only charges you for the month of January. You were required to give him proper notice of moving. Since you didn't tell us where you are or what the original lease stated, we can't tell you what proper notice is.

But its likely to be at least 30 days.

Everyone will tell you that you owe for a full month, me too. However, not knowing what that first lease said about auto renewal it could have renewed as a full years lease. What was the anniversary date of the first lease?