The black carbon (BC) component of ambient particulate matter is an important marker for combustion sources and for its impact on human health and radiative forcing. Extensive data archives exist for the black smoke metric, the historic measure of ambient particle darkness. An expression presented in earlier publications (Quincey, 2007; Quincey et al., 2011) for estimating BC concentrations from traditional black smoke measurements is shown to have limitations that can be addressed by using a more systematic approach to the issue of corrections for increasing darkening of the filter. The form of the more general relationship is shown to be an off-axis parabola rather than the on-axis parabola of the earlier work. Existing data from co-located black smoke and aethalometer measurements at 5 UK sites are reanalysed in this context. At very low concentrations of dark particles (British Black Smoke index <~10 ug m-3) a simple linear relationship BC (/ ug m-3) ≈ 0.27.BSI-BRITISH will suffice. A paraboli