Let's start with a definition: A paragraph begins at a new line. It is a group of related sentences that describe a central idea and a grammatical unit.
Is that helpful? No?
You're not alone. Don't know where to set the break? Confuse beat with scene with paragraph? Sounds familiar?
Word -> Sentence -> Paragraph -> Beat -> Scene -> Chapter -> Story
See what I've done here? I broke up the big mountain of work that's a story into ever smaller units. The smallest for our purposes is a word. Go smaller and you reach spelling; but that's beyond the scope of this article.
Words form sentences form paragraphs form beats form scenes form chapters form... story. Easy, right?
Well, no. If it was so easy, you wouldn't be reading this article. Believe it or not, the distinction has to do with time.
Yes, I mean time. But let's start at the beginning. We want to express a continuing stream of reality, because that is what our minds are accustomed to. Fiction is suspension of disbelief, after all.
There's this sensory, highly subjective world your main character occupies. Your reader has never met this person you're about to introduce him to, and now he's going on an intimate journey. And what is a journey? A sequence of change: internal (character) change as well as external (plot) change. The word 'Story' might be used as synonym for 'change'.
Let's assume your story is designed to make the most of conflict. If story equals change, change equals... what? Physics dictate that every action has a reaction, and that means you have cause and effect. Words on a page don't overprint each other: By their very arrangement left to right you see them passing from one to each other. Action, reaction. Cause, effect. One thing happens, then another thing, then another thing. Ideally. Such a sequence is a beat. Until the next unit-that-is-a-beat. Not helpful?
But then there's time. There's chronological, objective time and emotional, subjective time. As writer, you can play with both of them. Ever reduced a journey to a laconic 'After two weeks, they arrived in Moscow'? Or the opposite 'My heartbeats come one at a time, like droplets dripping from a leaky faucet'.
If the situation is tense, time races. And you can translate tension into space: The more words, the more relaxed your viewpoint character is. Long sentences and paragraphs describing scenery and the reader can just experience the timelessness of this particular afternoon.
But any change in external affairs telegraphs the possibility of danger. Something changes and your character has to react. Your character is forced to adjust, depending on how dangerous he judges the situation to be (i.e. a soldier sleeps through shelling while his comrade runs for the bunker). Change doesn't always involve progress, but progress always involves change.
If you consistently track internal and external time, your reader will experience the character's 'person' more than he could with any kind of character questionary, because in-built time and hence the sense of danger is a very personal characteristic. Your reader will see the fictive person as 'real'. You'll put him in your character's shoes.
And when change happens, this is when you place a paragraph break.
A scene organises conflict elements. It telescopes them, intensifies them, and gives them a sense of time. You don't have a continuing climax. You can slow time (emotional reaction, internal debate, yes, even flashbacks) and speed them up again; build towards a curtain fall.
You control story pacing by the way how you dole out action-reaction time. I hope you begin to see how paragraphs pertain to time. Follow action-reaction and at change put a break. It's that easy. Or at the change between external to internal. Or at punchpoints that you want to resonate with the reader. External time and internal time, action and reaction: Internal reaction (astonishment) or external beats (rubs eyes), integrate and intersperse them between each other. Ultimately, it's about time.
A beat equals a unit of story time, and paragraphs equal a smaller subset thereof.
You can use sentences in the context of time as well. Shorter sentences one after another will leave your reader gasping for breath, longer compound ones will ground him in description. And yet the effect of sentence length is not clear cut: In furious action, compound sentences will string together time in an unbroken string to be experienced by the reader heartbeat after heartbeat, giving a sense of urgency. But as with all things in writing, don't overdo it. Diversity is the name of the game.
Equally, there is no rule how long a paragraph should be. Play with paragraph breaks; they don't bite. Look out for when action pauses, in the real life as well as in your story. When is it time to draw 'breath'? When is an action over and a reaction starts? One sentence or five, to a total of 2 or 200 words, the only guidance is your reader, because a long wall of text looks as intimidating as the time it takes to read it (here we are again on the subject of time), while a two-word paragraph packs a punch.
Reference: 'Techniques of the Selling Writer' (Dwight V. Swain)