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UPS - Uninterruptible Power Supplies: A UPS goes between your wall outlet and a 120V device you want to keep running when the power from the electric company goes out. 
Small UPS are usually made to run only half an hour to 1 hour depending on the load and the internal components heat up after that time. Better go for a sinewave inverter which can run computers with large battery. I got a 9Ah battery for my old Beklin UPS to power a modem and router with a combined 1A power requirement. It should theoretically run for 9 hours, but there is overhead with the inverter (DC to AC conversion). It only ran for 4 hours. Battery Chargers and Jump Start batteries: These can be used as UPS's for 12V components like routers and modems by wiring them between your power socket and the device. These devices do not have 120 V AC power, so are more efficient for devices which will run on 12V (routers and modems) because it doesn't require an inverter which is inefficient.
5 Best lithium battery chargers 2021 - Gmund Cars
The 15 Amp Victron Blue Smart IP65 15A below was much larger but doesn't list AH. It was the choice in the Video below by a guy who also had a NOCO and wanted something more. 12 V Modem and Router backup power: The TalentCell Mini UPS Uninterrupted Power Supply 4.227000mAh 98Wh Lithium ion Backup Battery with DC 12V/9V/5V Output $65. 4.2 (283) It will power a modem and router which take a 12V DC input and also has usb outputs. One user got 12 hours powering a router and modem. This is listed as 27000 mAh which is true, but at 3.7v At 12 volts. It's really 8800 mAh. 1 person reported the battery exploded.
Shanqui Mini UPS Battery Backup Uninterruptible Power Supply for WiFi, Router, Modem, - rating 4.4 (1116) $50 Marbero 222Wh Portable Power Station, 60000mAh Backup Battery Pack with 4 DC Ports(12V) 4.2 (43) $129,
VA vs AH. UPS' is rated in VAs(or in Watts. The output VA or watts mean is the maximum power. e.g. you can't run a 800 W heater on a 750 VA UPS. Watts is energy. Watt-hours is energy. a 9AH battery will support a 1 amp load for 9 hours. However converting from DC to AC takes some energy, so you will probably only get 4 hours of AC at 1 amp. The most common are Battery Backup units which switch from direct power to battey in in 4-8 ms. A "True" UPS runs off batteries constantly so there is no switchover time. The 4-8 ms. switchover does not affect most computers. Battery life is typically 3-6 yrs. See UPS
Typically 100 watts of supplied UPS power will run 100 watts of incandescent lightbulbs, but only 71.4 watts of a typical capacitor input switching type computer power supply, and nearly 100 watts of a PFC computer power supply.
Batteries will last longer (more discharge cycles) if discharged at a lower rate. Battery RunTime Conext Battery Backup 300VA/180 Watts - 170 Watts 4 min 100 Watts 11 min. 500VA/300 Watts - 201 Watts 4 min/ 100 Watts 15 minAPC
True Power (watts) = Volts (RMS) x Amps (RMS) x Power Factor where V = Volts, A = Amps pf = the power factor of the load, applies to all electrical loads.
A standard 120 V household current swings between +170 V and -170 V in a sine wave pattern. the RMS value (root-mean-square) is 1/SQRT(2), or about 0.707 times the peak. This despite the fact that the average value of a sine wave is about 0.637 times the peak. In the case where the load acts purely resistive, such as that of an incandescent light bulb, heater or a PFC (Power Factor Corrected) switching power supply, the pf will equal 1 or nearly 1. For all other cases, the pf will vary between 0 and 1, and for a typical capacitor input switching type computer power supply, a power factor of about 0.714 is usually exhibited. Typically 100 watts of supplied UPS power will run 100 watts of incandescent lightbulbs, but only 71.4 watts of a typical capacitor input switching type computer power supply, and nearly 100 watts of a PFC computer power supply. Example: A typical capacitor input switching computer power supply is 200 watts. The VA output equivalent can be calculated as follows:
watts = VA * pf, or, VA = watts / pf so 280 VA of the UPS supplied power will be needed by the 200 watt computer power supply at full draw. Another faster way to express this, is
Computer Power Supply in Watts * 1.4 = UPS VA AC Watts to DC Amps AC Watts divided by 12 x 1.1 = DC Amps Some appliances or tools, such as ones with a motor, require an initial surge of power to start up ("starting load" or "peak load"). Once started, the tool or appliance requires less power to continue to operate ("continuous load"). So, power inverters (DC battery to AC) and generators are sometimes rated by peak and continuous load. Source: The Volt-Amp to Watt conversion information above came from a web site named Sutton Designs (www.suttondesigns.com/doctext/pf.html) which is no longer available.
DC Inverter: e.g. It will require 10 amp hours of battery to operate a 100 watt bulb for 1 hour. The battery rating should be twice this (i.e. 20 amp-hours for maximum battery life and performance.
Meters: Amp, watt, volts 12 V Connectors: There are 3 common types of connectors for 5-12 V devices: EC5 with 10 - 14 AWG used in battery chargers and batteries for RC cars, hellicopters, ....
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