  By combining our theoretical calculation and recently measured electric
quadrupole hyperfine structure constant of the $3d ^2D_{5/2}$ state in the
singly ionized $^{43}$Ca, we determine its nuclear quadrupole moment to one
percent accuracy. The obtained result, $-0.0444(6)b$, is about ten percent
improvement over the considered standard value. We have employed the
relativistic coupled-cluster theory at single and double excitations level to
calculate the electronic wave functions. The accuracy of these wave functions
are estimated by comparing our calculated magnetic dipole hyperfine constants
with their corresponding available experimental results of many low-lying
states. We also present hyperfine structure constants for other higher excited
states where experimental results are not reported. Role of the Breit
interaction has been investigated in these properties.
