# How long will an 6000 mAh battery pack power a 12v 60W amp for?

I could use some help calculating how long my battery will last. I’ve tried multiple online calculators.

Speakers: Peavey Monitors with 10 inch woofer, 1.4 tweeter ~ 101 max SPL

Amp: Pyle PFA200 60-Watt Class-T Hi-Fi Audio Amplifier with Adapter

Battery: TalentCell Rechargeable 12V 6000mAh/5V 12000mAh DC Output Lithium Ion Battery Pack

Using this milliamps to watts calculator, I put in 6000mAh and 12v and get 72Wh.

Since my amp requires 60 watts, shouldn’t it last for just roughly a bit over an hour?

I’ve been playing the speakers fairly loud off of this charged pack and it doesn’t seem to be losing so fast. I think I’ve already listened 6+ hours on just this charge.

What am I missing in my calculations? How long should these speakers really be able to go loud on this battery pack?

• This isn't easy- Audio has high peak power, but even at relatively loud volumes the average power is much lower. You would likely have to characterize your amplifier's draw with your typical source material and listening volume in order to get an accurate estimate. – John D Aug 10 '17 at 17:49
• @JohnD That typical source material usually works out to 1/8 average, both for bursted and pseudo random pink noise. Also, does OP play at full clip volume? – winny Aug 10 '17 at 17:55
• @winny Good rule of thumb, but with today's hyper-compressed mastering (which fortunately is finally easing off) some material can be higher, but well-mastered acoustic or classical can be lower. Of course the OP's volume level is key to the question as well..... – John D Aug 10 '17 at 18:06
• @JohnD I designed multi-kW PA audio amplifiers for a living some years ago and rig and mix concerts when I'm not in office. The "best" way to blow mains fuses, stall generators and/or smoke out bad amplifer designs due to too high average or just low Crest factor are: Enya, dubstep from 2008 and Chemical Brothers - Under the influence. – winny Aug 11 '17 at 12:12
• @winny Awesome :) – John D Aug 11 '17 at 15:41

I’ve been playing the speakers fairly loud off of this charged pack and it doesn’t seem to be losing so fast. I think I’ve already listened 6+ hours on just this charge

Your amp can output 60 watts but if you are not dumping 60 watts into your speakers it won't be taking 60 watts from your battery. Even on full volume, music has an average power level (compared to peaks) that is about 10 to 15 dB down so, if your peak is 60 watts (a big slice of kick drum) then your average power might only be about 4 watts.

Given that your amp may be 50% power efficient the input power into your amp may be, on average, about 8 watts.

In the example above the peak is 2 watts yet the average is only 63 mW so. if your peak is 60 watts, the average will be about 2 watts. However compressed music like hip-hop or drum and bass will be more like 12 dB in terms of crest factor ($\dfrac{P_{PK}}{P_{AVG}}$).

If you happen to be listening to classical music it might be an even bigger ratio. Are you listening to classical music on a battery powered hifi? I could make a guess of course!

What do you think the amplifier is doing when it's not producing sound? Just chugging watts? -- The 60 watt marker is what it can produce. If you would play a sine wave at maximum volume then it would draw 60 W constantly, but music doesn't contain max volume all the time, there's high volume here and there, and you're not blasting it at 100%.

Take this image for an example:

If you look at the maximum volume which happens somewhere in the middle. That's where the 60W are being drawn. Now look at the area, compare the black area compared to the white area if you imagine a rectangle going from left to right and maximum amplitude to the negative maximum amplitude. I'd say the black covers about 10-20% of that. So there's not much energy that needs to be produced for you to listen to music.

Here's some rough numbers that I'm naming on top of my head. About 10% will be the music, so 6W with your amplifier at maximum volume. If you lower the volume to say $\frac{1}{5}$ then it will draw on average $6W×\frac{1}{5}=1.2W$.

Compare that 1.2W to the 60W you started with. I'm ignoring the impedance in your speakers and the losses in the wiring and all other parasitic resistances/capacitances/inductances. So 1.2W is just an approximate.

If we revisit your equation at the start and replace 60W with 1.2W, then you should imagine that you can listen for $\frac{72Wh}{1.2W}=60h$. That's the same as using it for 2½ days constantly.