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A 110 watt motor is equal to a 1 amp motor... Versus a 12 amp motor, the 12 is more powerful. You've probably confused 110 watts with volts, as a 1 amp motor could not be used in a vacuum (it's too small).

Basically the amount of power is dependant on the amps the motor uses. You only have the spec on 1 motor so we can't answer your question. All vacuum motors are 110 volt.
You are trying to compare Apples and Oranges.

Amps or Amperage is a measure of electrical current.

Watts is a measure of electrical power.

When dealing with single phase power, which is most common in residences, the two are related by the following formula:

Watts (W) = Volts (V) x Amps (A)

Further we can be certain that the voltage is 120V since we are talking about a vacuum cleaner that would plug into a standard 120V household outlet.

A motor drawing 12 amps at 120V will produce 1440W under ideal conditions.

You can now compare apples to apples. 1440W vs 110W, however all this tells you is that 12amp device generates more power.

It dose not conclude that it provides more suction. For this you need to consider the efficiency (eff) of the devices.

1440W x eff = suction power

110W x eff = suction power

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