  Tunneling time, time needed for a quantum particle to tunnel through a
potential energy barrier, can be measured by a duration marker. One such marker
is spin reorientation due to Larmor precession. With a weak magnetic field in
$z$ direction, the Larmor clock reads two times, $\tau_y$ and $\tau_z$, for a
potential energy barrier along the $y$ axis. The problem is to determine the
actual tunneling time (ATT). B{\"u}ttiker defines $\sqrt{\tau_y^2 + \tau_z^2}$
to be the ATT. Steinberg and others, on the other hand, identify $\tau_y$ with
the ATT. The B{\"u}ttiker and Steinberg times are based on average spin
components but in non-commuting spin system average of one component requires
the other two to fluctuate. In the present work, we study the effects of spin
fluctuations and show that the ATT can well be $\tau_y +
\frac{\tau_z^2}{\tau_y}$. We analyze the ATT candidates and reveal that the
fluctuation-based ATT acts as a transmission time in all of the low-barrier,
high-barrier, thick-barrier and classical dynamics limits. We extract this new
ATT using the most recent experimental data by the Steinberg group. The new ATT
qualifies as a viable tunneling time formula.
