Given a number field
K
K
of degree
n
K
n_K
and with absolute discriminant
d
K
d_K
, we obtain an explicit bound for the number
N
K
(
T
)
N_K(T)
of non-trivial zeros (counted with multiplicity), with height at most
T
T
, of the Dedekind zeta function
ζ
K
(
s
)
\zeta _K(s)
of
K
K
. More precisely, we show that for
T
≥
1
T \geq 1
,
|
N
K
(
T
)
−
T
π
log
(
d
K
(
T
2
π
e
)
n
K
)
|
≤
0.228
(
log
d
K
+
n
K
log
T
)
+
23.108
n
K
+
4.520
,
\begin{equation*} \Big | N_K (T) - \frac {T}{\pi } \log \Big ( d_K \Big ( \frac {T}{2\pi e}\Big )^{n_K}\Big )\Big | \le 0.228 (\log d_K + n_K \log T) + 23.108 n_K + 4.520, \end{equation*}
which improves previous results of Kadiri and Ng, and Trudgian. The improvement is based on ideas from the recent work of Bennett et al. on counting zeros of Dirichlet
L
L
-functions.