Hi everyone: I love using Tasha's formula for creating new PC races that aren't over- or under-powered. And I'd love to find a simple formula for creating homebrew monsters by CR. Otherwise I feel unsure whether what I'm creating is too powerful or not powerful enough for my players. Does such a *simple* formula exist?

Yes- the dungeon master's guide has a section on creating monsters that match CR, and I think Xanathar's might also have some info.

*simple* ha,how could one conceive of that.The dmg has some general guidelines for monsters,and more importantly teaches how special abilities may affect cr.Xanathars has no monster balancing advice,it has some other cool stuff though.Tasha's also has no guide lines on race creation,so I have no idea what your talking about (lineage is it's own race,and also basically just variant human,and it's also overpowered.).

The simplest way is to find a monster of the same challenge rating, and change a few things. Replace attacks with attacks that deal close to or the same damage, use the same hp and use the same ac and the CR shouldn't change or not change that much. 

A less 'simple' way to create a monster based on what CR you want to give the monster can be done using the Create a Monster Section in the DMG. Say we want to create a meat shield style enemy. We want it to have: A CR of 4, lowish AC, high hp, medium size and we also want it to have the barbarians 'rage' ability for good measure. We want it to be equally as good at surviving and dealing damage if possible. We can create this in the following way:

1. Head to the 'Monster Statistics by Challenge Rating' and go down the rows until you reach the desired CR. We'll start with the defensive CR. Using this table we can work out a CR 4 monster 'typically' has 116-130hp.
   
   
2. However we want a monster with low ac as well, lets say... 12ac. If we look at the table it says a CR4 monster should typically have 14ac. Having less ac than the expected ac 'might' lower the defensive challenge rating. To see if it would, look at the expected ac for the next CR down, the expected ac for a CR 5 monster is 15ac. Because the ac we want to give the monster is 3ac less than that expected ac, then we know the defensive challenge rating would be reduced by 1. This means if we want a CR 4 monster we actually want to give it the hp of a CR5 monster, that would be 131-145hp. 
   
   
3. However our creature has the rage ability. Because they'll be more than likely to rage immediately, we can assume that rage is the equivalent of having resistance to bludgeoning, piercing and slashing damage. If you scroll down the Create a Monster Section, you'll see that a monster with an expected challenge rating of 4 with at least 3 resistances has an effective hp twice as much as their maximum hp. So if we want our creature to have an effective hp of 131-145, their maximum hp would be 66-72hp.
   
   
4. Next we need to check what the expected damage of a CR 4 monster is, if we look at the table it says the expected average damage is 27-32. We'll keep the attack bonus the same as the expected attack bonus for a CR 4 monster (+5) for now. Now that we know the average damage, ac and hp we can start to build the statblock further.
   
   
5. What sort of attack deals 27-32 damage, how about 2 attacks that deal 14-16 damage. Our rage ability increases the damage of attacks by +2, removing the 2 +2's means we want the damage of the attacks to equal 10 - 12 damage. There are a few ways to get this damage in an attack: (Greatsword) 2d6+3/4/5, (Greataxe)1d12+4/5/6. As we made the attack bonus +5 and we know the prof bonus for a creature under CR5 is +2, we know the strength modifier for this creature is +3. Therefore the Greatsword option is the perfect fit, we could always go back and change the attack bonus, but for now we'll leave it.
   
   
6. Now how does a creature get 66-72hp? As it's a medium creature we know its hit dice will be a d8. This bit requires a bit of maths to work out. Lets assume our constitution modifier is +2, now we have to work out how 70 can be made with 1d8+2 (6.5hp). 71.5 is equal to 6.5 x 11, therefore 11d8+22 hp would equal 71hp (Monster hp gets rounded down). Now we know our monsters hit dice.
   
   
7. Now how do we get 12ac. We can have a creature have a dex mod of +0 have a natural armour bonus of +2, we can have a creature with a dex mod of +0 wear hide armour or we can have a creature with no natural armour bonus have a dex of +2. There are other methods but we'll go with the natural armour bonus and +0 dex mod as our wall of meat isn't very mobile.
   
   
8. Now that we've added all the traits, the action, the hp, the armour etc. Nothing we do will change the Challenge Rating, so everything from now on is flavour. We still need to give our monster an Int and Wis score, so we'll go for 7 and 8 respectively to show his less than stellar planning skills. We need to give our creature a speed, we'll go with the standard 30ft. We'll set the language as common, the monster type as Humanoid and the passive perception to 9 (based on wis). And that's our statblock created.

This is a fairly simple example, and you need to keep an eye out for traits that will affect your creatures challenge rating such as flight, saving throw proficiencies or pack tactics. The Create a monster section tells you how 'most' of these traits affect CR. Remember if you want a very offensively powerful CR 4 monster, you can aim to give it an offensive CR of 6 and a Defensive CR of 2.

While I've used the DMG to do the hand calculations in the past I've since recently started to use CR Calculator which applies those rules in an automated result. 

Thanks! This may be as simple as it can get, and I appreciate it

THanks!

Thanks for the reminder about DMG!

"Tasha's also has no guide lines on race creation,so I have no idea what your talking about (lineage is it's own race,and also basically just variant human,and it's also overpowered.)." Call it what you will, but I've used it to homebrew races for a couple of NPCs where I needed something different.