Should "So", "Therefore", "Hence", and "Thus" be followed by commas?

Often, I have come across sentences that begin with "So". Should such an usage of "So" be followed by a comma?

Are the following examples correct.

1. He is very good at computers. So, I think he can fix your computer.

2. When we multiply an even number with another even number, the result is an even number. So, the square of an even number is an even number.

What happens if we choose to use "Therefore", "Hence", or "Thus" instead of "So"? Do the rules still remain the same?

1. When we multiply an even number with another even number, the result is an even number. Therefore, the square of an even number is an even number.

2. When we multiply an even number with another even number, the result is an even number. Hence, the square of an even number is an even number.

3. When we multiply an even number with another even number, the result is an even number. Thus, the square of an even number is an even number.

• On the use of commas, and on punctuation in general, I recommend, as I have before, this guide written by Larry Trask. Commented Feb 23, 2012 at 15:58
• There is a "rule" that says that, like And and But, So should never begin a sentence. But people do it all the time. And that's fine. So don't worry about it.
– slim
Commented Feb 23, 2012 at 16:09
• @slim: So, we'll take that as implicit support for not adding a comma after "so", then? Commented Feb 23, 2012 at 16:48
• @BarrieEngland Can you summarize the answer to the OPs particular question (about a comma after an initial entry word) in your answer? Otherwise, this doesn't say anything other than give a reference. Commented Feb 23, 2012 at 18:59
• @BarrieEngland, The answer to my question isn't there in the link you have provided. Commented Feb 24, 2012 at 17:53

Commas are not determined by grammar, nor by which words they follow. Comma indicates a particular intonation. If you would use that intonation in speaking the sentence, use a comma; if not, don't. So it's important to hear what you're writing, in your mind if nowhere else.

Generally in short sentences you wouldn't, but if the sentence following the introductory word is long, you might well. Also generally speaking, if the material coming first is long (as it is in this sentence but wasn't in the previous sentence), you would.

Punctuation is not absolute; it's a work in progress.

• I think in OP's context, including the comma reflects a certain degree of "hesitant attention-grabbing" - often typical of some people's conversational style within a group. It causes the "So" to linger longer before the "follow-up" conclusion - implicitly there's a pause there that means something like (please start listening to me now because I'm about to say something relevant to what's just been said) Commented Feb 23, 2012 at 16:56
• That's certainly one recognizable usage. There are lots of others, along with myriads of individual styles, not all useful. As I said, a work in progress. Commented Feb 23, 2012 at 18:28
• Haha - it'll be a lifetime's work, I think! But I certainly think your point about "Generally in short sentences you wouldn't" covers many situations. Conversely, I find it hard to imagine anyone saying, for example, "It's raining, so, here's an umbrella". Commented Feb 23, 2012 at 20:19
• This theory of commas is not particularly helpful, as it simply converts the question into "Should introductory words be spoken with a comma-like intonation?" There are answers to that in formal registers, and these correspond to rules for comma usage. Commented Mar 8, 2017 at 10:27
• There are some answers to that in some formal registers, and these correspond to some rules for comma usage, for some people. But in the last analysis, writing does not capture all (or even most) of language, and no punctuation rules solve that problem. You have to hear the intonation, as I said in the answer. Commented Mar 14, 2017 at 14:14

The short answer is "no." The longer answer is: a comma is not a requirement but neither is it something to avoid.

What may blow your mind is that the comma is not required anywhere in any of your examples. It is a matter of style.

The trend is away from commas, and I use them where they help make the sentence easier to read, or help the flow. More important is consistency. If the comma is omitted in one place, it should be omitted in all instances thereafter. Useful punctuation is invisible; the reader shouldn't notice it.

Short answer: Commas after introductory words are allowed, but not required.

As mentioned in the comments, Larry Trask's guide to punctuation is an excellent resource. Introductory words like the ones you mention (also "moreover", "in contrast" etc.) fall into the category of bracketing commas. Trask's summary of the rules for including bracketing commas are:

• Use a pair of bracketing commas to set off a weak interruption which could be removed from the sentence without destroying it.
• If the interruption comes at the beginning or the end of the sentence, use only one bracketing comma.
• Make sure the words set off are really an interruption.

Introductory words are primarily used to smooth the transition between sentences, so they can clearly be removed from the sentence without changing the meaning. Thus, they fulfill Trask's criteria for bracketing commas used at the beginning of a sentence.