what is proper cut off voltage for my battery??

It looks like a Sealed Lead Acid (SLA) deep cycle battery based on the picture. If you can confirm this, then go with the guidelines for that type of battery. See the table under "Deep Cycle Battery" for battery life as it relates to Depth of Discharge:

https://batteryuniversity.com/learn/article/lead_based_batteries

As far as voltage as it relates to Depth of Discharge, see this article here:


You will note that at 11.8 volts a deep cycle battery is already discharged 100% (state of charge = 0%). Also note that these voltages are the no-load voltages. When the load is attached the voltage will sag, but when the load is removed for a period of time the voltage bounces back up and that is the voltage used to determine Depth of Discharge. You will have to experiment to see which load voltage corresponds to the no-load voltage for the Depth of Discharge you are targeting. The load voltage will vary with the size of the load itself. For best longevity of the battery you shouldn't discharge it more than 30%, but if you want to give up some battery life for greater run time then you can make a compromise. Just understand that in general the deeper the discharge the shorter the battery life, but the article states that in order to get the best value out of the battery you shouldn't really discharge below 50%
 
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