What is the formula used in calculating how much to raise?

Say I am playing 1-2 NL on a 9 handed table.

4 Limpers and I am on the button with AKs.

4 limpers = 8 dollars
The blinds = 3 dollars
Total =11 dollars

I would raise to 15 dollars without much reasoning.

Am I correct?

Obviously I don't know much poker.

There is no formula because there is no one size fits all approach in poker.

Easy example to illustrate that: CO raises 3BB, you are on the BU with AA. If you knew that CO would never call a reraise or 4bet, you'd always call. If you knew he would call a 3bet of 12BB but not 13BB, you'd reraise 12BB. If you knew he would call all-in, you would do that.

In online games, most players have some standard sizing they use absent other information. In live games, players usually tend to call much more and also larger bets than online. Making it $15 with AKs might be a good sizing here, if at least one of the limpers hates to fold preflop, $20 or even $25 might be the way to go. A couple of years ago, it wasn't uncommon for somebody to make it $30+ against a bunch of limpers at 1/2 live.

So, it's important to think about the reason for every action at a poker able. What is your goal by raising with AK on the button?

It's an easy statement to make, but isn't the goal in poker maximize profit while minimizing losses? So, what's your goal with a raise on the button (the answer is different in different situations)? Are you trying to take down the pot preflop? Are you trying to get called by worse hands? Do you want to limit the field or are you looking to invite others into the hand?

In my opinion, your raise on the button should be limiting the field while getting hands you dominate (Ax, Kx) to play the hand. Raising to $15 often eliminates certain hand ranges, unless you're playing with loose players and then you have to take that into account if they call your raise. You'd much rather have KQ or AJ call you preflop than 64 or 97 or a hand like that. Of course, the hand range for players who call you is something you need to learn based upon how they play other hands.

Who do you think calls you at $15 in this scenario? What line are you going to take if you miss the flop and it checks to you on the button? What line are you taking if you flop an ace and a guy bets into you? What line are you taking if you flop an ace and it checks to you? What raises have you seen people call preflop? Are standard opening raises in this game to $12-15? Only $8-10? or bigger like $18-25? All these questions are things you need to consider when raising in this scenario.

As madlex said, "There is no formula because there is no one size fits all approach in poker." Every scenario, every game, every table is different.

Online, this is easy. You just press the POT button and it comes to $15.
If working out a pot-sized raise is too complicated, just use your standard open sizing (for an unopened pot) and then add 1bb per limper, as this will get you in the right ballpark.

e.g. If you normally open for 3bb ($6), then you can add 4bb ($8) to that for the 4 limpers, to make it $14. If your standard open size is 4bb ($8) because you live in 2013, then $8 + $8 = $16.

If you don't think $14 or $15 will narrow the field to an acceptable size, then going a bit bigger might work better.

1) You bet 'enough' to accomplish your goal for the bet. The answer will be different based on 'which' players limped and what the table dynamic is at the time. Last night I was opening for $18 on a 1/2 table and getting 3-4 to the Flop on most occasions. There are other nights when $11 gets everyone to fold .. even a UTG limper.

You are very correct to consider who (and how many) have limped, but don't forget their stack sizes as well. You may not want to get into a spot where you are forced to call-off or fold to a marginal fold-equity shove.

2) You bet to protect your range as well. It's important to treat AK the same as 66, especially when in position (like when you are on the Button), so that you can take down some 'free' money when you miss the Flop but feel that you can generate folds based on your strong consistent image. It's hard to hit the Flop .. and just because you missed doesn't mean your opponent hit. You may very well still have the best hand and be betting for value. GL