Carson's Rule states that the occupied band width is equal to two times the deviation plus the highest modulation frequency. As a formula:
BW = 2 ( f(d) + f(m) )
The highest modulation frequency for two-way communications is generally accepted to be 3 kHz.
So, the bandwidth for 5 kHz deviation would be 2 ( 5 + 3 ) = 16 kHz. For 2.5 kHz deviation, it's 2 ( 2.5 + 3 ) = 11 kHz.
I am not the one who originally posted this my comments are the ones in BOLD. That said, here goes.
The FCC has a different way of specifying the BW, (They use a spectral mask). The BW they state, is. 20 KHz for GMRS and FRS should be 12.5 KHz. This is to fit into a mask. Carsons Rule perhaps does not account for noise plus distortion products and thus a splatter filter sometimes is required. Plus when trying to cut off any voice energy, especially after being pre-emphasized, at 3,000 Hz no low pass filter is perfect. So Carson's Rule, in my opinion is good theory, that falls a bit short of practice,
Confusing all of this is the fact that radios will be certified with 20K0F3E and 16K0F3E emissions in GMRS Part 95 (and legacy Part 90).
Why 20 KHz BW inside a 25 KHz channel spacing? Additional protection for frequency error of the transmitter and receiver plus uncertainties in receiver filter BW.
§ 95.1773 GMRS authorized bandwidths.
Each GMRS transmitter type must be
designed such that the occupied
bandwidth does not exceed the
authorized bandwidth for the channels
used. Operation of GMRS stations must
also be in compliance with these
requirements.
(a) Main channels. The authorized
bandwidth is 20 kHz for GMRS
transmitters operating on any of the 462
MHz main channels (see § 95.1763(a)) or
any of the 467 MHz main channels (see
§ 95.1763(c)).
(b) Interstitial channels. The
authorized bandwidth is 20 kHz for
GMRS transmitters operating on any of
the 462 MHz interstitial channels (see
§ 95.1763(b)) and is 12.5 kHz for GMRS
transmitters operating on any of the 467
MHz interstitial channels (see
§ 95.1763(d)).
(c) Digital data transmissions. Digital
data transmissions are limited to the 462
MHz main channels and interstitial
channels in the 462 MHz and 467 MHz
bands.
§ 95.573 FRS authorized bandwidth.
Each FRS transmitter type must be
designed such that the occupied
bandwidth does not exceed 12.5 kHz.