The s-wave scattering length (a) is an important parameter in ultracold collisions and precision tests of fundamental physics, yet its accurate calculation remains a challenge. Solving suitable vibrational Schrödinger equations with scaled interaction potentials and reduced masses, the relationship between the binding energy (D₀) of the highest vibrational state and the s-wave scattering length is derived for a set of ground state Sr₂ isotopomers. The resulting “a versus D₀” relations are robust even if approximate potentials are used, thus enabling reliable scattering lengths to be determined directly from experimental binding energies. The presented approach will have broad applicability, notably when an accurate potential is unavailable and when the literature (semiclassical) counterparts of the probed “a versus D₀” relations become inadequate.