when you type "help buttord" in matlab you get:
BUTTORD Butterworth filter order selection.
[N, Wn] = BUTTORD(Wp, Ws, Rp, Rs) returns the order N of the lowest
order digital Butterworth filter that loses no more than Rp dB in
the passband and has at least Rs dB of attenuation in the stopband.
Wp and Ws are the passband and stopband edge frequencies, normalized
from 0 to 1 (where 1 corresponds to pi radians/sample). For example,
Lowpass: Wp = .1, Ws = .2
Highpass: Wp = .2, Ws = .1
Bandpass: Wp = [.2 .7], Ws = [.1 .8]
Bandstop: Wp = [.1 .8], Ws = [.2 .7]
BUTTORD also returns Wn, the Butterworth natural frequency (or,
the "3 dB frequency") to use with BUTTER to achieve the specifications.
[N, Wn] = BUTTORD(Wp, Ws, Rp, Rs, 's') does the computation for an
analog filter, in which case Wp and Ws are in radians/second.
When Rp is chosen as 3 dB, the Wn in BUTTER is equal to Wp in BUTTORD.