Are all sentences below correct?

* I parked in the parking lot.
* I parked on the parking lot.
* I parked at the parking lot.

My understanding is that I can use "to park in" if the parking lot is indoors and "to park at" with any kind of parking lot, but I'm not sure if "to park on" is usual for both indoor and outdoor parking lots.
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When talking about a structure for holding cars, such as a lot, you park *in*. "I parked in the lot." "I parked in the parking garage."

You can also talk about parking *on* a surface or *on* a street/road. "I parked on the concrete". "I parked on 4th Avenue." "Parking on grass is not good for your car."

In this sense, saying you parked "on the lot" is also acceptable (but not as common) because the lot is a surface. You never park *on* a parking garage or other fixed structure that your goes goes inside of.

You can also park *at* a location or destination. "I parked at the store." In this case, the store is your destination. This is a more colloquial way of saying "I parked in the store's parking lot."

In the same sense, you could say you parked *at* a lot or a garage, since they are also locations. "I parked at the lot on 5th Street." sounds natural. The lot on 5th Street is a location that you parked at.

This can get even more complicated: If you parked in a parking garage located on 6th Street, you could say "I parked on 6th Street" and then clarify with "in the parking garage."

In some cases, all of these are interchangeable. If a friend asks, "where did you park?", you could say "At the lot on 5th Ave" OR "On the lot on 5th Ave" OR "In the lot on 5th Ave". Any of these works because in this situation, the lot could be considered either a location or a surface/structure for cars.
> 
> I parked in the parking lot.
> 
> 
> 

This is correct whether the parking lot is enclosed in some way or not (it doesn't matter). The use of "in" here generally means "within the borders of". This is also the same sense you would use when saying "I parked in a parking space" as well.

> 
> I parked on the parking lot.
> 
> 
> 

This is not common usage for parking lots. It's grammatically correct, but the use of "on" emphasizes the idea of "on top of", and most parking lots don't actually have a "top" (they're open-air spaces with no roofs), so it seems a bit odd to say this. However, it is common to say something like "I parked on the asphalt" or "I parked on the street", because those are flat things you can put a car on top of.

> 
> I parked at the parking lot.
> 
> 
> 

This is also fine. This is using "at" in the sense of a location which you went to and then you parked there.

In general:

* "in" is the most common way to say this, and you can use it really any time you are inside of some area with well-defined boundaries (e.g. "in the parking lot", "in the yard", etc)
* "at" is also fine, and would not sound particularly strange in most situations.
* "on" would sound strange to most people.