So.... Normally you'd build the thing and then calibrate it using test signals and a known-good SPL meter as a reference.
There are companies that calibrate scientific equipment, but proper calibration would cost you about as much as purchasing an SPL meter. If you just need something "useful", but not necessarily scientifically-accurate, you can calibrate it yourself with test tones (or pink noise) and a known-good SPL meter.
calculate the dbm from a mic out put of 2.7 to 5 v ?
You can look-up the microhone sensitivity spec. That will give the voltage (in millivolts) for a given SPL level. Then, you have to compensate for the preamp gain. The specs for an ordinary recording/performance mic are just a guideline. You can get a calibrated instrumentation microphone that comes with the actual test results for that specific unit. [u]This[/u] is the least expensive calibrated mic I know of ($50 USD). They generally go for a LOT more.
...bird sounds range from 50hz to 200 khz as far as we know,
Is that a typo? 200kHz would be a problem. You'd probably need a 2nd special ultrasonic transducer for that, and since it's above the normal audio range, you'd have to devise a method of calibrating it... That would require some "serious science"...
The good thing is that the Arduino itself doesn't need to go to 200kHz. You can use an analog "averaging circuit" to convert the high-frequency AC signal to varying DC. For my (uncalibrated) meter lighting effects, I use a [u]Peak Detector circuit[/u]. You'd probably want something where the DC follows the average level, rather than the peaks. That can be done with a low-pass filter (or something like a low-pass filter). But, that also means that any weighting has to be done in analog, since there is no frequency-information going into the Arduino.
If a bird actually makes sounds up to 200kHz, I would guess it's also making lower frequencies at the same time. Those lower frequencies will mask (drown-out) the supersonic frequencies anyway. You'd have to do spectral analysis to detect the high frequencies..... A single "loudness" measurement isn't going to do it. And unless you are in a soundproof studio, there will be lots of other ambient sounds masking those frequencies (and maybe even drowning-out audible bird sounds). High frequencies are also greatly attenuated in air, so if there is much distance, the supersonics won't be measurable.
What bird goes down to 50Hz? An ostrich?