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Yes. How much depends on the radio. Heres a few examples.

1: Old car, with a radio that only puts out 20x4 watts of power RMS. Not much of a draw on power, so your alternater isnt under much more stress with it. Noticable, probably not. Were talking fractions of miles per gallon

2: My 98 Ford Mustang GT with a mach 460 sound system (Factory) Ok, so the stock radio puts out 54x4 watts of power. Nothing noticable, but then it powers 2 amps, 1 160watt, and one 300 watt for the subs. A bigger difference. I actually notice a difference in gas milage on long trips. About 1 - 2 MPGs.

3: I have a 2010 Ford Fusion that I just put a sound system into. 54x4 watts in the head unit, factory amplified (dont know the specs) and then a 300.1 Kicker amp (rated at up to 600watts). Now, under full load, everything turned up this thing draws alot of power and notice a huge drop in gas milage as well as power. Im talking about 5Mpgs.

This is what happens. As the car starts to draw more power, the alternator knows that it needs to apply more friction in order to supply the draw. The alternator gets harder to turn, and the motor has to work that much harder to turn the alternator to supply the power. Therefore you will use more gas with a louder sound system.

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