Is there an equation exists to tell the relationship b/w sins and happiness??

I am not going to talk about religious beliefs, but about matters so obvious that we see in real life. it has gone out of style to mention them though but the fact is good deeds still pay, you may not get instant results though. I don't think you should worry about theory as long as the man does what it's supposed to do- The good even if people laugh, but I believe in my neighbors, my relatives and my partner. I know their faults and good part and I know that their good virtues simply outweigh their faults so it could not be a formula for me but whatever you think sometimes or always, the good deeds always bring the best results. Let them laugh who find it a laughing matter.

Your own conscience is the best judge of your deeds. Always depend upon it,

This depends on mental state. If the sinner is really sorry for his sins, he will feel guilty and suffer mentally. Moreover if his sin is also an offense under law, he may face legal consequences as well. On the other hand, if some one is okay with what he does, he will not suffer for any sin. For example, eating meat and extra marital relation is considered sin. If somebody is okay with these, he will have no feeling of guilt and so not suffer.

Sins and Happiness are like two sides of a coin. When you toss the coin, its not possible to get both the sides of the coin. Either sins or happiness. But not both at a time.
Sins may yield pleasure, but not happiness, Remember pleasure in temporary while happiness is divine and permanent.

I believe in the adage, "We will reap what we sow."
Just try this.
Keep a pebble on a table. And say, Hey, Pebble, move on. Pebble will not care and stays at the same place where you kept. Now, try this. Just give a light push, the pebble obediently moves ahead.
Same thing applies here.If you want an outcome, you should act. If you want a positive out come, you should act positively. Remember Newton proved it in his law of gravitation that for every action there will be a reaction. I add every positive action there will be a positive reaction.

Yes, it is true at least this is what have observed. I have seen many people who are not of a good disposition or don't do the ideal things yet they are the happiest beings on this earth,definitely they must have done something good in their past which is giving them benefit now.

Also, I have experienced..sooner or later the sinner is punished. No matter how hard you try to escape..so yes sins and happiness are complementary to each other.