df numbers in lmer

Hello,

I'm wondering how to obtain df-s associated with t values for fixed factors
in lmer. I need them in order to calculate the effect sizes (Pearson's r)
for those fixed factors.

One method of calculating df number I came across is to take the total
number of observation minus the number(s) of levels of random factor(s). But
I have my doubts, such as

(1) what about the number of fixed factors in the model - shouldn't it be
subtracted as well?

(2) I can see how this method can be applied to models where random factors
are crossed with fixed factors but what about when they are nested? Or in
case of more comlex designs? The model I'm struggling with at the moment is
such:
I have 10 females and 10 males crossed in a full factorial design, resulting
in 100 offspring trait means (one per each pairing). Fixed factors are:
female category and male category (2 levels each). I'm fitting a model:

siz <- lmer(sz~femcat+malecat+(1|femid)+(1|maleid))

What about those df-s for femcat and malecat?

I'd be very grateful for advice as well as literature suggestions (I'm very
new to mixed modelling and trying to get my head around it).

-Zofia