So I'm working on a species of tiny humanoids. They are about 13cm tall and are not that different from humans apart from their size.
Would their gestation period be different, and how much?
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There is a good science article that discusses the gestation times of mammals compared to weight and most importantly explains that the larger an animal is, the longer the gestation is going to be due to a special case of the square cube law - a creature that is larger can only get a smaller percentage of nutrients through the umbilical cord by body size. It also shows some comparisons of other mammals with weight and gestation times to show that there is a level of correlation.
That, though, is only part of the picture.
Your small humanoids are going to suffer from a range of problems that may make them less ideal in an environment they share with normal sized humans. For the purposes of this answer, I'll discuss only two that are perhaps the most relevant if any comparison to conventional humans needs to be made.
1) They will run hot.
Mammals are warm blooded creatures, meaning that they need to maintain a constant internal temperature. This gives them the advantage of being active even in the cold, but the price is an increased metabolism that requires more food in colder environments. That said, the larger the animal is, the better it handles this requirement because the surface area (square cube law again) is a much smaller fraction of the volume of the animal, meaning that it can retain internal heat better and therefore survive in cold weather with a lower proportional increase in food. It also means that its metabolism can be slower, and it doesn't have to stay as warm inside as smaller creatures.
The price of the higher metabolism smaller mammals have to maintain is of course shorter lifespan - their metabolisms are proportional to the rate at which the creature ages. This is why mice live such short lives, elephants live so long and both have almost exactly the same count of heart beats in their average lifespan. (This correlation isn't universal across all mammals, BTW.)
The practical upshot of this is that your smaller humanoids are going to have to run 'hot' by comparison to normal humans, meaning they will eat more (proportionally speaking) and die younger as their metabolisms burn out faster.
2) Intelligence and Brain Size
To be fair, no scientist worth their salt will ever claim to tell you that they know exactly how the brain works, where the consciousness resides in it and how our intelligence is contained within it. BUT, what we do know about human intelligence is that it seems to be the manifestation of a very complex network of neural cells acting in concert and that our intelligence is in some respect at least a function of the complexity of that network.
In point of fact, the human brain accounts for around one quarter of the daily energy requirements of a human body. Nature abhors waste and inefficiency so there is a strong argument that our brains are no more complex than they need to be in order for our intelligence to manifest in the way it does. Of course the problem is that your smaller humanoids now face a dilemma; either they have a brain of similar size and complexity meaning they are intelligent but at the cost that their brains are consuming more than 99% of their energy resources and their heads are effectively acting as a 'ball and chain' for them, anchoring them to a single location, or they are less intelligent.
Can they manifest some form of reasoning and intelligence with smaller brains? Possibly but there is also an argument for them being less capable of the advanced insights born of our own human intelligence by virtue that the complexity of their minds is not as advanced. This does not mean they could not adapt the tech that humans bring them to their own use, or even negotiate and engage in diplomatic relations with us (they are probably still capable of language), but they will not be as capable of grasping advanced abstract models that we take for granted in our technically enabled lives.
Your smaller humanoids are likely to have similar gestation times and lifespans of rats, which are similar in size to what you describe. They may be intelligent, but their size restricts their intelligence to some degree, although we cannot be sure in science by how much because to my knowledge we have not done such research and potentially don't have any way to conduct it even if we wanted to.
Your humanoids may well be tool users and capable of language but compared to larger organisms they will suffer both advantages and disadvantages. Lower gestation rates may be a benefit, but the other side of that coin is reduced lifespan and potentially reduced total intelligence capacity.