Electronic – Calculation of noise in Non inverting Op-amp circuit

I think, what you have overlooked is, that when you basicly multiply the 10Hz bandwidth with the 6nV, you get an rms voltage.

According to Paul Horowitz, experiments have shown, that the peak-peak-voltage is about 6 times the rms-voltage. So when you mulitply the 18nVrms by 6, you get about 99nVpp.

TI is quoting a spec based on the total noise in the audio range (20 Hz-20 kHz, presumably), adjusted based on a standard A-weighting curve (see http://en.wikipedia.org/wiki/A-weighting for more, as well as figure 22 of the TI data sheet.) -89 dBv is what you'd see if you looked at the noise on a scope, after passing it through a filter with that particular response. Something on the order of 30 microvolts.

To compare that value to the MAX9814's specification, you can multiply 30 nV/root-Hz by sqrt(20 kHz-20 Hz) to get 4.3 microvolts of total noise in the audio spectrum.

This is all complicated by the fact that the volts-per-root-Hz concept assumes constant noise power per 1 Hz of bandwidth. This will not apply at offsets near DC where the noise takes on a 1/f characteristic, and neither manufacturer gives explicit information about their part's 1/f corner frequency. With these two chips in particular, you need to compare them via the one spec they both provide: the A-weighted SNR (60 dB for the TI part, 64 for Maxim.)