i want to reformat my computer...i know i should make backups (done)...but what happens to my Steam account...will i be able to install it again...I'm saying this because i read the terms and conditions and they said do not install the game to a different computer...it might be the same process of me installing it again in another computer(which will be my computer still,after reformatting)so what will it be?

I've never really used STEAM but Shadow Master (now Zero) has formatted his pc before and was still able to use STEAM, so no worries. Steam is by an online account, and you can download your games with that account,regardless of which pc.