  The dipolar (magnetostatic) interaction dominates the behavior of spin waves
in magnetic films in the long-wavelength regime. In an in-plane magnetized
film, volume modes exist with a negative group velocity (backward volume
magnetostatic spin waves), in addition to the forward surface-localized mode
(Damon-Eshbach). Inside the film of finite thickness $L$, the volume modes have
a nontrivial spatial dependence, and their two-dimensional dispersion relations
$\omega(\mathbf{k})$ can be calculated only numerically. We present explicit
perturbative expressions for the profiles and frequencies of the volume modes,
taking into account an in-plane applied field and uniaxial anisotropy, for the
regimes $\lVert \mathbf{k}L \rVert \gg 1$ and $\lVert \mathbf{k}L \rVert \ll
1$, which together provide a good indication of the behavior of the modes for
arbitrary wavevector $\mathbf{k}$. Moreover, we derive a very accurate
semianalytical expression for the dispersion relation $\omega(\mathbf{k})$ of
the lowest-frequency mode that is straightforward to evaluate using standard
numerical routines. Our results are useful to quickly interpret and control the
excitation and propagation of spin waves in (opto-)magnetic experiments.
