  Nuclear quadrupole moments ($Q$s) in three isotopes of potassium (K) with
atomic mass numbers 39, 40 and 41 are evaluated more precisely in this work.
The $Q$ value of $^{39}$K is determined to be 0.0614(6) $b$ by combining the
available experimental result of the electric quadrupole hyperfine structure
constant ($B$) with our calculated $B/Q$ result of its $4P_{3/2}$ state.
Furthermore combining this $Q$ value with the measured ratios $Q$($
^{40}$K)$/Q$($ ^{39}$K) and $Q$($ ^{41}$K)$/Q$($ ^{39}$K), we obtain $Q$($
^{40}$K)$=-0.0764(10) \ b$ and $Q$($ ^{41}$K)$=0.0747(10) \ b$, respectively.
These results disagree with the recently quoted standard values in the nuclear
data table within the given uncertainties. The calculations are carried out by
employing the relativistic coupled-cluster theory at the singles, doubles and
involving important valence triples approximation. The accuracies of the
calculated $B/Q$ results can be viewed on the basis of comparison between our
calculated magnetic dipole hyperfine structure constants ($A$s) with their
corresponding measurements for many low-lying states. Both $A$ and $B$ results
in few more excited states are presented for the first time.
