20 amps on the circuit will trip it unless it is is broken. Then it may trip with a lower current or not at all... Any resistance added to the circuit from a bad or dirty connection will add to the total current causing it to trip sooner than expected.
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A 20 amp breaker will trip if the current exceeds 20 amps for an extended period of time. It is designed to protect the circuit from overheating and causing a fire hazard. So, it would take more than 20 amps to trip a 20 amp breaker.
The rating on the handle of a breaker is the trip amperage. So to answer your question, it takes 20 amps to trip a 20 amp breaker. This is the same theory with all breaker amperage numbers.
If the current safety requirement is 30 amps, you can;t run if off of a larger circuit breaker. It violates NEC and is very unsafe. If the current requirement is 40 amps , it will continuously trip a 30 amp breaker because it is too small of a breaker in electrical requirement.
It usually takes more than 15 amps to trip a 15 amp breaker, as breakers are designed to protect against overcurrents. However, factors like ambient temperature, length of wiring, and type of load can affect this. It is recommended to consult the manufacturer's specifications for the exact values.
On a 15 amp breaker, you can draw up to 120 volts in a standard residential circuit. The voltage remains constant at 120 volts, but the amperage capacity is what is limited by the 15 amp breaker.
It is likely that the 15 amp tool is drawing more current than the breaker can handle, causing it to trip. The GFCI outlet might not be the issue here unless there is a ground fault causing it to trip. Consider using the tool on a circuit with a higher amperage breaker to prevent tripping.
In a typical US automobile, a 30 amp fuse will sustain a constant load of 360 watts. Fuses and circuit breakers perform on an "I squared t" rule. For example, a 30 amp fuse will not blow on 31 amps for a very long time. A 20 amp breaker can take anywhere from 10 minutes to two hours to trip on 25 amps. We simply dumb it down so that laymen and technicians need not make mistakes. Power on seven 100 watt light bulbs simultaneously. That means a circuit suddenly provides 50 amps. 50 amps does not trip a 15 amp or 20 amp breaker, again, due to the "I squared t" rule. A 50 amps load only exists for tens of milliseconds. Not long enough. A 30 amp continuous appliance will not trip a 30 amp breaker. But a safety margin means limiting 30 amp appliances to 26 amps or less. Meanwhile, an 18 gauge lamp cord wire typically rated for 10 amps will actually conduct up to 50 amps continuously. Again, that wire is oversized for other safety reasons. And to keep it simple. These concepts apply to fuses vehicles and structures.