Assuming information about the mean velocity and vertical turbulent velocity, it is possible to calculate the flow direction wavenumber spectrum of pressure fluctuations ϕ(k1 δ)/τ02δ. The law of the wall plus Cole's wake function represented the mean velocity profiles. A scale-anisotropic model of R22 was used and the component intensity û2 was assumed to vary across the boundary layer in constant proportionality to the Reynolds stress. Calculated zero-pressure-gradient spectra rise as k11.5 at low wavenumbers. Curves for various Reynolds numbers are closely similar, and diverge only slightly around the peak in the spectrum. A high wavenumber spectrum ϕk1v/u*. u*/τ02v is independent of Reynolds number. The calculations reveal an overlap region in which ϕ ∼ k1−1. Imposing an equilibrium pressure gradient increases the spectrum at the low and mid wavenumbers, but has no effect in the overlap region. The spectrum peak for II = 6 is a factor 102 higher than for the zero-pressure-gradient layer. It is proposed that the convective velocity Uc(k1) has an overlap region. The overlap law is found to be \[ \frac{U_c}{u_{*}} = -\frac{1}{\kappa}\ln k_1\delta +\frac{1}{\kappa}\ln\frac{u_{*}\delta}{\nu}+A, \] where K and A are the same constants as in the mean velocity expression. Comparison with experiments shows very good agreement. A rough convective ‘wake’ function is formulated for the low-wavenumber range. Wavenumber spectra are converted to frequency spectra, and compared with experiments. Data from a zero pressure gradient and an adverse pressure gradient II = 3 show reasonable agreement with the calculations.