# Force produced by muscles proportional to area or volume?

I've heard it said that the force a muscle can exert is proportional to its cross-sectional area. It seems to me it should be proportional to length also. If you have someone pulling on a large block, you could increase the force by getting another person to pull in parallel, OR by attaching a rope to the block and having both of them pull in series on that one rope. So shouldn't muscle strength be proportional to both area and length, making it proportional to volume?

Does the answer have to do with the fact that material strength is proportional to cross-sectional area, so this puts a limit on the amount of force that muscles can exert without breaking?

• sounds more like theory than reality. Sure, there is correlation between sectional area of muscles and force exerted, but proportionality? I think anyone hitting a gym knows better. Dec 13, 2019 at 5:36
• @Umaxo Well, there are other factors of course that would have to be considered in a real situation. When talking about a proportionality between two variables you assume that everything else is held constant. Dec 13, 2019 at 5:41
• "you assume that everything else is held constant" and of course changes are small enaugh to use first term of taylor series:) I just think that in reality such simple relationship cannot hold. This is in contrast to the proportionality of p~T in ideal gass. Yes, you need to keep volume and particle number constant and it is not the most exact formula, but it can be used in real situation pretty well. It just seems to me, in the case of muscles, such simple relationship is useless anywhere else than textbooks. But i might be wrong Dec 13, 2019 at 6:29
• @Umaxo I think it would be useful when roughly estimating strength difference between animals of hugely different size, like insects and humans, because the change in area is so great that it makes a really big difference. It's probably not super useful for figuring out strength differences between humans or anything like that. Dec 13, 2019 at 6:37