I'm not an expert at this topic, so there might be some mistakes in my explaination. Basically, output impedance acts like a resistor, connected in series to your transducer (iem / headphone / speaker). Now when resistor is connected in series, the bigger resistance will take up more voltage. So if for example you have a 3 ohm output impedance connected to the SE846 which has 5 ohm resistance @ 4khz, the output impedance will take 37.5% of the voltage supplied by the amp. Compare this to having 0.5 ohm output impedance connected to the same thing. (0.5 ohm IMO is the highest output impedance any dedicated DAP should have) The output impedance will only take 9% of the voltage supplied from the amp. A pretty big difference, isnt it? Low impedance headphone / iem is known to be "current hungry", as opposed to the high impedance headphones that has "voltage hungry" trait Oh for additional note, BA driver iems are notorious for their impedance swings. For example, SE846 is rated at 8 ohm, but its lowest impedance is 5 ohm. So, objectively speaking you want the highest output impedance to be 1:10 ratio, based on tyll's statement in his pono review

If you have a low output impedance amp, even if it doesn't say it can drive 8 ohms on the spec sheet, it'll probably be fine.

If you actually look carefully at the report for this technical test: http://www.head-fi.org/t/608553/review-comparison-two-flagships-pass-in-the-night-sony-xba-4-review-vs-the-mdr-ex1000-updated-with-7550-and-xba-40#post_8357374 You will find that if finds 5 ohms, not 1 ohm to be the minimum impedance of the XBA4. Still tough for your typical headphone amp, but since we have many speakers that have impedance curves this low building a headphone amp to drive the pants off of it should be far from impossible. In fact is has probably been done many times in the form of a low powered high quality amplifier for driving small speakers in small environments.

How do you calculate how much current an amp is capable of with just the power spec? For example, the jds labs element is 1.5w peak power into 32 ohms. Can you get a max current from that?

see, that's what I originally was thinking. But when I applied it to some amps with given max current values, it didn't work out. Like the O2 amp is 200mA but the power spec of 613mW at 33 ohm gives 136mA. The fiio e11k is 92mA, but the power spec of 450mW into 16 ohm gives 167mA.

The spec gives the absolute maximum under any condition. The calculation gives the maximum under a given condition.

for the O2 the only time I've seen 200mA mentioned it was peak current!!! what we usually deal with as power and voltage are RMS values. so sqrt(0.613/33)= 0.136rms indeed, but 0.136/0.7=0.194A peak and that's pretty much your 200mA from specs. about the e11k I just can't find any load associated with those 92mA(can't access fiio's website at all), but when nothing is written, it's often into 32ohm(or 16ohm or whatever, when it's not written it's just useless specs in the end). but it so happens to fit nicely with 32ohm this time ^_^ power is 270mW into 32ohm so I=sqrt(0.27/32)=0.0918A for 16ohm you'll get another limit.

Oh, okay, so I was thinking that the peak current was constant no matter what load. So, atm, if you were wondering if you had enough current or power for a certain headphone at a certain volume, the only way you could know is if the amp manufacturer gives you specs for that specific load?

really need a I,V graph - but sometimes you can guestimate most properties of an amp's output limits from hi and low Z output power spec points - if hi Z power is limited by power supply Voltage/output stage Vswing and lo Z drive limited by max output current with more different load Z power specs sometimes you can even see evidence of output Z - some headphone amps have 10s of Ohms - the Senn HDVD amp is reputed to have 40 Ohms in series with its output

My amp which is a SET tube amp recommends 33 ohm impedence headphones. Headphone I plan to get is rated at 8 ohms impedence. Will there be lot of distortion? would it be ok?

Depends on the headphone but I guess there will be quite some distortion, as most very low earphones have huge FR differences when not optimally impedance-matched.

A quick hypothetical question. If I was considering an amp, with a recommended headphone impedance of 32ohm- 600ohm. Does that mean it would damage a pair of headphones rated at 25ohms? I'm looking at getting a pair of AudioQuest's Nighthawks down the road and trying to find a balanced amp to pair with them.

It should be fine. The one concern would be if the amp's output impedance is greater than a couple ohms, but even then it wouldn't damage the 25 ohm headphones (it just would not necessarily drive them without audible artifacts/changes to the sound).