I have a little trouble reconciling the claims in this thread...
1. Apple specs claim 30mW per channel headphone out on virtually all of their audio devices (iPad, iPods, iPhones).
(verified with Apple specs)
2. Measured rms output voltage 1.1V (peak V = around 1.556 based on that).
3. Most headphones have a 1Khz impedance between 8Ω and 32Ω. (http://www.soundonsound.com/sos/jan03/articles/impedanceworkshop.asp) and most small-jack headphones come in the 16-32Ω range (based on observation, experience, and reading a fair number of spec. sheets)
So... Getting to the reconciliation issues...
Ohm's law sates that P=EI and V=IR (where P is power in Watts, E is pressure in Volts, I is Current in Amps, and R is Resistance in Ohms).
The whole point of having a characteristic impedance of a device is so that we can treat it as resistance for calculations and assume that the effective impedance is roughly the same across the intended frequency range. (The difference between resistance and impedance is that resistance is DC resistance, so no frequency or phasing effects need to be considered. Impedance is the effective resistance at a given frequency. For audio devices, usually 1Khz.)
So, if we have 1.1V and let's take a middle of the road 24Ω (half-way between 16Ω and 32Ω) headphones, we get the following results:
I=E/R = I=1.1v/24Ω = I=0.04583333=45.8mA
P=IE = P=0.0458333 * 1.1 = 0.05041666 which is a little more than 50mW/channel.
OTOH, if we assume 30mW per channel and work backwards from there:
P=IE = 0.03W =I * 1.1v = 0.0272727A = I
I=E/R = 0.0272727A=1.1V/R = 0.0272727A*R=1.1V = R=40.3333737Ω
So it seems either the devices are able to deliver 50mW/channel, or, they are expecting 40Ω headphones, both of which seem extraordinary.
I'm perfectly willing to accept that I may well have gotten something wrong here and I would appreciate it if anyone can show me what.