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Alas, as SevenSidedDie points out in the comments, The RAW doesn't really answer your question.

I can see arguments that depend on the situation, but this is a personal opinion, not RAW...

If a spell requires concentration, then the caster should have a fairly solid idea of how long they can hold that concentration before the spell drains out and is done. GM's call if that's literally to the round, but generally, I'd argue that yes, they know. This is your Precision Knowledge category.

However, sometimes, a spell might slide down into Imprecise Knowledge. Certainly if the spell isn't a concentration-based spell. A fire-and-forget spell, the caster should know with a high, but not perfect, degree of accuracy. Of course, the higher the caster level, the more precise. I could see some kind of house-rule requiring Arcana checks if the exact timing was important, or risk being off by up to 5% or something. But really, I'd avoid this generally, since Precision Knowledge is easier to manage at the table, if for no other reason. RAW has no such rules, implying Precision Knowledge is the intended mode of play.

And some cases should be No Knowledge. If you didn't cast the spell, then you shouldn't know exactly how long it will last. Period. You may assume it will last X rounds. And a Arcana check might refine your estimate to a higher degree of accuracy... Same for scrolls or other "canned" spells. Again RAW does not indicate such a thing, implying Precision Knowledge is the intended mode of play. But as a GM, if my PCs didn't have a way to know exactly how long someone else's spell would last, they wouldn't know.

But given that RAW doesn't provide frameworks for a PC to check the duration, the implication is that you just know.

Edit to add: Another situation that, as GM, I'd argue could force a situation from Precision to Imprecise or from Imprecise to No Knowledge would be anything that interferes with focus/concentration/situational awareness.

If your attention is distracted in some way, your ability to keep precise track of everything going on around you could slip just enough to throw off your count. Imagine counting a stack of coins. But while that's going on, people are trying to kill each other and you. There's a chance you would lose count. Now, your PC has (theoretically) trained to resist those distractions, so it wouldn't happen every combat. But any spell or effect that could cause you to lose concentration should also be able to make your "count" of the duration slip, just a bit.

That's not a RAW situation at all. But it is one I could see coming into play in a high stress situation. But not as a sudden arbitrary GM call. Maybe as a house rule.

Alas, as SevenSidedDie points out in the comments, The RAW doesn't really answer your question.

I can see arguments that depend on the situation, but this is a personal opinion, not RAW...

If a spell requires concentration, then the caster should have a fairly solid idea of how long they can hold that concentration before the spell drains out and is done. GM's call if that's literally to the round, but generally, I'd argue that yes, they know. This is your Precision Knowledge category.

However, sometimes, a spell might slide down into Imprecise Knowledge. Certainly if the spell isn't a concentration-based spell. A fire-and-forget spell, the caster should know with a high, but not perfect, degree of accuracy. Of course, the higher the caster level, the more precise. I could see some kind of house-rule requiring Arcana checks if the exact timing was important, or risk being off by up to 5% or something. But really, I'd avoid this generally, since Precision Knowledge is easier to manage at the table, if for no other reason. RAW has no such rules, implying Precision Knowledge is the intended mode of play.

And some cases should be No Knowledge. If you didn't cast the spell, then you shouldn't know exactly how long it will last. Period. You may assume it will last X rounds. And a Arcana check might refine your estimate to a higher degree of accuracy... Same for scrolls or other "canned" spells. Again RAW does not indicate such a thing, implying Precision Knowledge is the intended mode of play. But as a GM, if my PCs didn't have a way to know exactly how long someone else's spell would last, they wouldn't know.

But given that RAW doesn't provide frameworks for a PC to check the duration, the implication is that you just know.

Another situation that, as GM, I'd argue could force a situation from Precision to Imprecise or from Imprecise to No Knowledge would be anything that interferes with focus/concentration/situational awareness.

If your attention is distracted in some way, your ability to keep precise track of everything going on around you could slip just enough to throw off your count. Imagine counting a stack of coins. But while that's going on, people are trying to kill each other and you. There's a chance you would lose count. Now, your PC has (theoretically) trained to resist those distractions, so it wouldn't happen every combat. But any spell or effect that could cause you to lose concentration should also be able to make your "count" of the duration slip, just a bit.

That's not a RAW situation at all. But it is one I could see coming into play in a high stress situation. But not as a sudden arbitrary GM call. Maybe as a house rule.

Alas, as SevenSidedDie points out in the comments, The RAW doesn't really answer your question.

I can see arguments that depend on the situation, but this is a personal opinion, not RAW...

If a spell requires concentration, then the caster should have a fairly solid idea of how long they can hold that concentration before the spell drains out and is done. GM's call if that's literally to the round, but generally, I'd argue that yes, they know. This is your Precision Knowledge category.

However, sometimes, a spell might slide down into Imprecise Knowledge. Certainly if the spell isn't a concentration-based spell. A fire-and-forget spell, the caster should know with a high, but not perfect, degree of accuracy. Of course, the higher the caster level, the more precise. I could see some kind of house-rule requiring Arcana checks if the exact timing was important, or risk being off by up to 5% or something. But really, I'd avoid this generally, since Precision Knowledge is easier to manage at the table, if for no other reason. RAW has no such rules, implying Precision Knowledge is the intended mode of play.

And some cases should be No Knowledge. If you didn't cast the spell, then you shouldn't know exactly how long it will last. Period. You may assume it will last X rounds. And a Arcana check might refine your estimate to a higher degree of accuracy... Same for scrolls or other "canned" spells. Again RAW does not indicate such a thing, implying Precision Knowledge is the intended mode of play. But as a GM, if my PCs didn't have a way to know exactly how long someone else's spell would last, they wouldn't know.

But given that RAW doesn't provide frameworks for a PC to check the duration, the implication is that you just know.

Alas, as SevenSidedDie points out in the comments, The RAW doesn't really answer your question.

I can see arguments that depend on the situation, but this is a personal opinion, not RAW...

If a spell requires concentration, then the caster should have a fairly solid idea of how long they can hold that concentration before the spell drains out and is done. GM's call if that's literally to the round, but generally, I'd argue that yes, they know. This is your Precision Knowledge category.

However, sometimes, a spell might slide down into Imprecise Knowledge. Certainly if the spell isn't a concentration-based spell. A fire-and-forget spell, the caster should know with a high, but not perfect, degree of accuracy. Of course, the higher the caster level, the more precise. I could see some kind of house-rule requiring Arcana checks if the exact timing was important, or risk being off by up to 5% or something. But really, I'd avoid this generally, since Precision Knowledge is easier to manage at the table, if for no other reason. RAW has no such rules, implying Precision Knowledge is the intended mode of play.

And some cases should be No Knowledge. If you didn't cast the spell, then you shouldn't know exactly how long it will last. Period. You may assume it will last X rounds. And a Arcana check might refine your estimate to a higher degree of accuracy... Same for scrolls or other "canned" spells. Again RAW does not indicate such a thing, implying Precision Knowledge is the intended mode of play. But as a GM, if my PCs didn't have a way to know exactly how long someone else's spell would last, they wouldn't know.

But given that RAW doesn't provide frameworks for a PC to check the duration, the implication is that you just know.

Edit to add: Another situation that, as GM, I'd argue could force a situation from Precision to Imprecise or from Imprecise to No Knowledge would be anything that interferes with focus/concentration/situational awareness.

If your attention is distracted in some way, your ability to keep precise track of everything going on around you could slip just enough to throw off your count. Imagine counting a stack of coins. But while that's going on, people are trying to kill each other and you. There's a chance you would lose count. Now, your PC has (theoretically) trained to resist those distractions, so it wouldn't happen every combat. But any spell or effect that could cause you to lose concentration should also be able to make your "count" of the duration slip, just a bit.

That's not a RAW situation at all. But it is one I could see coming into play in a high stress situation. But not as a sudden arbitrary GM call. Maybe as a house rule.

Alas, as SevenSidedDie points out in the comments, The RAW doesn't really answer your question.

I can see arguments that depend on the situation, but this is a personal opinion, not RAW...

If a spell requires concentration, then the caster should have a fairly solid idea of how long they can hold that concentration before the spell drains out and is done. GM's call if that's literally to the round, but generally, I'd argue that yes, they know. This is your Precision Knowledge category.

However, sometimes, a spell might slide down into Imprecise Knowledge. Certainly if the spell isn't a concentration-based spell. A fire-and-forget spell, the caster should know with a high, but not perfect, degree of accuracy. Of course, the higher the caster level, the more precise. I could see some kind of house-rule requiring Spellcraft checks if the exact timing was important, or risk being off by up to 5% or something. But really, I'd avoid this generally, since Precision Knowledge is easier to manage at the table, if for no other reason. RAW has no such rules, implying Precision Knowledge is the intended mode of play.

And some cases should be No Knowledge. If you didn't cast the spell, then you shouldn't know exactly how long it will last. Period. You may assume it will last X rounds. And a Spellcraft check might refine your estimate to a higher degree of accuracy... Same for scrolls or other "canned" spells. Again RAW does not indicate such a thing, implying Precision Knowledge is the intended mode of play. But as a GM, if my PCs didn't have a way to know exactly how long someone else's spell would last, they wouldn't know.

But given that RAW doesn't provide frameworks for a PC to check the duration, the implication is that you just know.

Alas, as SevenSidedDie points out in the comments, The RAW doesn't really answer your question.

I can see arguments that depend on the situation, but this is a personal opinion, not RAW...

If a spell requires concentration, then the caster should have a fairly solid idea of how long they can hold that concentration before the spell drains out and is done. GM's call if that's literally to the round, but generally, I'd argue that yes, they know. This is your Precision Knowledge category.

However, sometimes, a spell might slide down into Imprecise Knowledge. Certainly if the spell isn't a concentration-based spell. A fire-and-forget spell, the caster should know with a high, but not perfect, degree of accuracy. Of course, the higher the caster level, the more precise. I could see some kind of house-rule requiring Arcana checks if the exact timing was important, or risk being off by up to 5% or something. But really, I'd avoid this generally, since Precision Knowledge is easier to manage at the table, if for no other reason. RAW has no such rules, implying Precision Knowledge is the intended mode of play.

And some cases should be No Knowledge. If you didn't cast the spell, then you shouldn't know exactly how long it will last. Period. You may assume it will last X rounds. And a Arcana check might refine your estimate to a higher degree of accuracy... Same for scrolls or other "canned" spells. Again RAW does not indicate such a thing, implying Precision Knowledge is the intended mode of play. But as a GM, if my PCs didn't have a way to know exactly how long someone else's spell would last, they wouldn't know.

But given that RAW doesn't provide frameworks for a PC to check the duration, the implication is that you just know.