# Converting from trace reversed to standard metric perturbation

In linearised gravity, when dealing with gravitational waves it is common to consider just the spatial part of the trace-reversed metric perturbation $$\bar{h}_{ij}$$.

I know that in general the trace-reversed perturbation is defined,

$$\bar{h}_{\mu \nu} = h_{\mu \nu} - \frac{1}{2} \eta_{\mu \nu} h$$

My question is, how explicitly do I convert e.g. $$\bar{h}_{xx} \rightarrow h_{xx}$$? I have a feeling that it is just a factor of $$2$$, e.g. Eq 6.26 of Carrol ?