J. W. Swan, M. M. Shindel, and E. M. FurstRupture, bond breaking, or extraction from a deep and narrow potential well requires considerable force while producing minimal displacement. In thermally fluctuating systems, there is not a single force required to achieve rupture, but a spectrum, as thermal forces can both augment and inhibit the bond breaking. We demonstrate measurement and interpretation of the distribution of rupture forces between pairs of colloidal particles bonded via the van der Waals attraction. The otherwise irreversible bond is broken by pulling the particles apart with optical tweezers. We show that an ensemble of the particle trajectories before, during and after the rupture event may be used to produce a high fidelity description of the distribution of rupture forces. This analysis is equally suitable for describing rupture forces in molecular and biomolecular contexts with a number of measurement techniques.