Why are conformational isomers considered as isomers?

I was taught that geometric (cis-trans) isomers are considered isomers because there is a high energy barrier to breaking the double bond for rotation (to convert into the other isomer).  

 Given that there is a low energy barrier to rotation about a single bond, why are conformational isomers considered as isomers? 




Gaurang's answer deals well with the theory part I just wanted to give a visual aid.




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![enter image description here](https://i.stack.imgur.com/QiMIR.gif)  

(Taken from [Atropisomerism of naphthyl alcohol](https://chemistry.stackexchange.com/a/89920))


Let's call the rotating substituent on the naphtahlene a fan.
The fan has two black fins one red fin.   
  

Now let us consider two conformations



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> Red fin at 3'o clock![enter image description here](https://i.stack.imgur.com/7aalbm.jpg)
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And 



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> Red fin at 9'o clock![enter image description here](https://i.stack.imgur.com/u3FLqm.jpg)
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If you were to take snapshots of both the conformations they look different.  

Now these two isomers **are** different and naming them as 9'o clock and 3'o clock is obviously very inefficient.  

That's why conformational isomers and their nomenclature exists, for us to point out specific configurations of a compound.


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> 
> I was taught that geometric (cis-trans) isomers are considered isomers because there is a high energy barrier to breaking the double bond...
> 
> 
> 


There's a problem here. Geometrical isomers are isomers because the arrangement of **different groups** around the pi bond is **different**. Consider the following molecule:


[![1,1-dichloropropene](https://i.stack.imgur.com/5bb0e.png)](https://i.stack.imgur.com/5bb0e.png)


It also has a pi bond, we might be tempted to say that they are geometrical isomers. But, they are not. In fact, they are identical. 


Also, geometrical isomerism can occur *without* a pi bond, as in 1,2-dimethylcyclohexane.


The actual condition for geometrical isomerism is the *restricted rotation* of different groups, leading to different isomers that can be *isolated* from each other. These isolated isomers usually have *very different* physical and chemical properties from each other, and the [Wikipedia page](https://en.wikipedia.org/wiki/Cis%E2%80%93trans_isomerism#Comparison_of_physical_properties) does a pretty good job of detailing that.




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Now, recall that geometrical isomerism and conformational isomerism are both forms of stereoisomerism. That is, they arise because the relative configuration of their atoms in *space* is *different*. 


You are correct that conformational isomerism arises because of *unrestricted rotation* of a molecule around its sigma bond. In fact, there are infinite conformations for any given molecule! Notice that I said *conformations*, because *conformational isomers* are finite, and refer to only those conformations that have specific energy minima or maximas. Here are, for example, the finite conformational isomers of butane:


[![energy of conformations of n-butane](https://i.stack.imgur.com/vxEzx.jpg)](https://i.stack.imgur.com/vxEzx.jpg) (*[source](https://chemistry.stackexchange.com/a/11020/5026)*)


The reason why these conformational isomers are given special study ("conformational analysis") is because ([to quote](https://en.wikipedia.org/wiki/Conformational_isomerism)) they "can be used to predict and explain product selectivity, mechanisms, and rates of reactions". Again, the Wikipedia page [details](https://en.wikipedia.org/wiki/Conformational_isomerism#Conformation-dependent_reactions) this nicely with examples.




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**To sum this up:**


* Both geometrical isomerism and conformational isomerism are a type of stereoisomerism
* Geometrical isomers are considered so because of restricted rotation (about a pi bond or a ring), wile conformational isomers have unrestricted rotation (about a sigma bond)
* Geometrical isomers are distinguished from each other because of their very different chemical and physical properties. Hence, they are considered as isomers and separately studied.
* Conformational isomers usually have similar properties, and rapidly interconvert. Yet, they are sometimes helpful in explaining the mechanisms of certain reactions. Again, they are considered as isomers and need to be studied.


I hope it helps!


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