A closed-form waveguide invariant β for a Pekeris waveguide is derived. It is based on the modal Wentzel–Kramers–Brillouin (WKB) dispersion equation and implicit differentiation, in conjunction with the concept of the angle-dependent “effective boundary depth,'' ΔH(θ). First, an explicit expression for β(m,n) between mode pairs is derived assuming an ideal waveguide of the effective waveguide depth H+ΔH(θ), which provides an excellent agreement with the exact value calculated for the Pekeris waveguide of depth H using KRAKEN. Then, a closed-form expression for a group of adjacent modes is derived: β = (H + ΔH)/(H/cos2θ − ΔH), which reduces to β = cos2θ as ΔH/H ≪ 1, the analytical expression for an ideal waveguide. For applications to source-range estimation, the waveguide invariant β is used to derive the theoretical beam-time migration (i.e., dispersion curve) in a Pekeris waveguide.