Most UPS has a small battery. Measure the voltage. If it's 12 to 13V you can plug an external car battery and it will last much longer (almost 10 times longer)
I just want to point out here for safety sake and educational use that a car battery is not a good idea for two main reasons.
1) They release toxic fumes. I can't remember the exact chemical. I believe it occurs while in a charging state. And if I can remember, is flammable.
2) A car battery is great for cars and other ignition systems since they provide that needed "high cranking Amp" ability for a few seconds. Long term drain is not so great. The cut off voltage is higher than a Lithium Iron Phosphate battery. (There's a type of rating for that. I can't remember it now).
I have a LeFePO battery and can run my scanner ("police scanner") on it for at least 22 hours straight. This battery is 6Ah. Doing the math of Amp consumption of around ~.250 mA from the scanner (that's with constant audio on high) that's around ~ 24 hours of contentious use from the battery. ( 6/.25 = 24).
These Lithium Iron based batteries are great for low current devices or a home brew UPS. For one, they're cut off voltage is a lot better, and the Lithium Iron versions are not prone to explode and catch fire like the Lithium Phosphate counterparts. These do have phosphate, but it's also iron. LiFePO4. Li = Lithium Fe = Iron Po = Phosphate. Again, they are pricey though. I picked up my Kastar 12V 6 Ah battery on eBay for around ~$40 bucks I think it was. The other great thing is that they have at least a 2,000 charge cycle. I think the other Lithium Phosphate batteries have that as well though. I can charge this battery from "dead" to full in about 1 hour and 37 minutes. I have been doing experiments on this thing and recording the data. LOL You have to use a LiFePo charger though. The one I have is a Fuyuang model FY1504000 which is apparently UL listed which is pretty good considering. You want UL listed electronics for safety reasons. I bought the charger on eBay as well.
Believe me when I tell you lots of stuff can be had on eBay cheaper and with free shipping over Amazon. It's just that shipping time may not be there. I really don't care. So long as I get the thing withen a week. LOL Very long time eBay user. First created my account in 2003. Well, I lost my password to that account and created a new one in 2005. I've seen on rare occasions eBay users since eBay first came about circa 1995! :O
And you should NEVER plug in a car battery into a UPS. The UPS charging circuity is ONLY meant for lead acid batteries and at that for a specific type meant by the manufacturer. Same applies with using a LiFePo battery in a UPS meant for lead acid batteries. You'll probably have a fire in no time if you try to charge a LiFePO battery with a lead acid charging circuit. The lesson here is if you're not a qualified electrician, competent amateur radio operator, or don't know a lot about electrical stuff, don't mess with it. If you do and fail, in the end it could be negligence on your part and when the house goes up in flames say goodby to the insurance payout.