Can the capacity of a battery be determined from Volts, Amperes, and output of Joules for xyz amount of time?

I'm trying to purchase a portable car battery charger (Noco Genius Boost) and I can't tell if it's possible to calculate the capacity in Ampere-hours or Watt-hours. The reason why I ask is because there is no indication of Ampere-hours or Watt-hours, or anything related to time.

The product information in the details show: 12V, 1000A, and output of 7000 Joules per 3 seconds.

Is the capacity possible to determine and if so, how did you calculate the math?

Normally the capacity of battery is specified by "Watt-Hour" written on the battery or in the battery datasheet. If this isn't specified, "Amp-hour" will be written on it. You can calculate watt-hour using this:

Watt-hour = Voltage x Ampere hour (specified on the battery)

E.g Battery voltage = 12v , Amp-hour=1000, then

watt-hour = 12 x 1000 => 12000 watts-hour.

what this means is that if the battery supply 12000 watts to your car/circuit, it will work for 1 hour (ideally though). 1 watt = 1 Joule/sec; so 7000joules/3sec => 2334 watts.

It means that it can supply ~2.3KW to the load. Now if you want to calculate the operating time of battery for a specific load, say, 200watt load, watt-hour/watt(load) => 12000/200 =>60 hours (theoretically)

Without knowing if that 3 second rating fully discharges the battery or if that is just the limit of the test rating, there's no guarantees on any calculations. Your best bet is to Google high C rating lithium ion batteries with similar physical dimensions and weight to see what it's closest to.

No. It is not possible to determine the capacity from the information given. Weigh the battery and compare the weight with batteries of similar weight and cost to get an estimate of the capacity.