There are few techniques capable of the non-destructive and model-free measurement at 1% absolute accuracy of quantity of material in thin films without the use of sample-matched standards. We demonstrate that Rutherford backscattering spectrometry can achieve this robustly, reliably and conveniently. Using 1.5 MeV He+, a 150 keV ion implant into silicon with a nominal fluence of 5 × 1015 As cm-2 has been independently measured repeatedly over a period of 2 years with a mean total combined standard uncertainty of 0.9 ± 0.3% relative to an internal standard given by the silicon stopping power (a coverage factor k = 1 is used for all uncertainties given). The stopping power factor of this beam in silicon is determined absolutely with a mean total combined standard uncertainty of 0.8 ± 0.1%, traceable to the 0.6% uncertainty of the Sb-implanted certified reference material (CRM) from IRMM, Geel. The uncertainty budget highlights the need for the accurate determination of the electronic gain of the detection system and the scattering angle, parameters conventionally regarded as trivial. This level of accuracy is equally applicable to much lower fluences since it is not dominated by any one effect; but it cannot be reached without good control of all of these effects. This analytical method is extensible to non-Rutherford scattering. The stopping power factor of 4.0 MeV lithium in silicon is also determined at 1.0% absolute accuracy traceable to the Sb-implanted CRM. This work used SRIM2003 stopping powers which are therefore demonstrated correct at 0.8% for 1.5 MeV He in Si and 1% for 4 MeV Li in Si.