Calculating headphone sensitivity
The essential parameter is the sensitivity of the driver, usually expressed in sound pressure level (dB) per watt of electrical (dB SPL/W), as measured by test equipment at 1 m. Typically this parameter is frequency sensitive.
In the case of the headphones in your comment, they give the specification "90 dB SPL at 0.13 mW". Like most specifications in the audio electronics industry, they omit details of test conditions. They don't give us the frequency range or distance at which this measurement was taken. Typically this parameter is given with a recording device at 1 m, but for reasons I'll explain, it's quite clear that was not the case here.
For now, let's assume they measured this at 4.5 cm, allowing 1 cm between the driver and outer ear, and 3.5 cm for the average depth of the ear canal in adults. Let's call it 90 dB SPL at 0.13 mW, 0.045 m, probably at 1 kHz but we'll ignore the effects of frequency.
Sound attenuates according to an inverse square law. We can calculate the attenuation factor in dB as 20 log(0.045/1) = –27 dB. Decibels are logarithms, so adding/subtracting them is multiplication/division of the real quantity.
Subtraction our attenuation of –27 dB, we now know that:
$$
90\space\mathrm{dB}\space\mathrm{SPL} @ 0.13\space\mathrm{mW},\space0.045\space\mathrm{m} =63\space\mathrm{dB}\space\mathrm{SPL} @ 0.13\space\mathrm{mW},\space1.0\space\mathrm{m}
$$
0.13 mW converts to –9.9 dBm or –39.9 dBW. To eliminate the "0.13 mW" component of this non-standard sensitivity, we subtract this negative factor, or rather add it, thus giving:
$$
63\space\mathrm{dB}\space\mathrm{SPL} @ 0.13\space\mathrm{mW},\space1.0\space\mathrm{m} =103\space\mathrm{dB}\space\mathrm{SPL/W}\space@\space1.0\space\mathrm{m}
$$
A standardized sensitivity of 103 dB SPL/W at 1 m converts to an efficiency of 12%. This sensitivity and efficiency is reasonable for a high end set of cans and probably typical for earbuds. Acoustic devices are, shall we say, resoundingly inefficient. Remember that when a loudmouth politician is yammering on about something.
The efficiency is so low, perhaps the industry prefers to not talk about it. Many loudspeakers can be around 80-90 dB SPL/W @ 1 m, with efficiency below 1%. Sensitivity is the parameter of interest, because our perception of loudness is roughly logarithmic, and it allows for a simple equation of speaker sensitivity (dB) + amplifier gain (dB) = loudness (dB). From there, you determine how much speaker and amplifier you need to hit a desired loudness.
Calculating efficiency from sensitivity
The conversion is simply:
Efficiency = 10^((Sensitivity in dB – 112)/10)
The dB SPL scale is a relative scale, with 0 dB SPL defined as 20 µPa of sound pressure or equivalently, 1 pW of acoustic power.
How do we know they didn't measure 90 dB SPL @ 0.13 mW, 1.0m? That converts to 130 dB SPL/W, or about 63% efficiency. The most sensitive drivers are only about 20% efficiency.
Caveats
Poor impedance matching between will reduce the power transfer from amplifier to headphones. As usual, ideally the output impedance of the amplifier is equal to input impedance of the driver.
Impedance is frequency sensitive as well.
