Can I use a car battery for an inverter, or vice versa?

Do you have this question? The simple answer is NO.

The car batteries(automobile batteries) and inverter batteries are built to work in a different way. You can definitely use a car battery and vice versa, but you are killing them. The battery which should last for years may become unusable in a matter of months or weeks.

Car batteries are built to supply high current/power for a short span of time. This is the requirement for an automobile battery. An automobile requires high power for cranking. This is required for a short time, usually seconds. Once the engine is fired up, the load on battery is almost nil as all the load will be taken over by the alternator.
The alternator charges the battery again and keeps the battery charge at the peak so that the battery is ready for next cranking requirement. Essentially an auto battery supplies a high power for few seconds, and will be charged immediately. In most cases the battery may never go below say 80% of its capacity as the battery will be immediately charged. These batteries are accordingly built. These batteries can not withstand going down to say 20% of capacity and then getting recharged which is typically the case in inverters.

Inverter batteries are built to supply constant power for a long time, they can go down to even 10% and then get charged to 100%. They are built to handle this deep discharge cycles, which auto batteries can not. These batteries are not built to supply the high cranking power required for auto batteries.

This article is only to give a basic idea of the batteries, the numbers used may not be correct.

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