Abstract. The formation of black carbon fractal aggregates (BCFAs) from combustion and subsequent ageing involves several stages resulting in modifications of particle size, morphology, and composition over time. To understand and quantify how each of these modifications influences the BC radiative forcing, the optical properties of BCFAs are modelled. Owing to the high computational time involved in numerical modelling, there are some gaps in terms of data coverage and knowledge regarding how optical properties of coated BCFAs vary over the range of different factors (size, shape, and composition). This investigation bridged those gaps by following a state-of-the-art description scheme of BCFAs based on morphology, composition, and wavelength. The BCFA optical properties were investigated as a function of the radius of the primary particle (a_o), fractal dimension (D_f), fraction of organics (f_organics), wavelength (λ), and mobility diameter (D_mob). The optical properties are calculated using the multiple-sphere T-matrix (MSTM) method. For the first time, the modelled optical properties of BC are expressed in terms of mobility diameter (D_mob), making the results more relevant and relatable for ambient and laboratory BC studies. Amongst size, morphology, and composition, all the optical properties showed the highest variability with changing size. The cross sections varied from 0.0001 to 0.1 µm² for BCFA D_mob ranging from 24 to 810 nm. It has been shown that MAC_BC and single-scattering albedo (SSA) are sensitive to morphology, especially for larger particles with D_mob > 100 nm. Therefore, while using the simplified core–shell representation of BC in global models, the influence of morphology on radiative forcing estimations might not be adequately considered. The Ångström absorption exponent (AAE) varied from 1.06 up to 3.6 and increased with the fraction of organics (f_organics). Measurement results of AAE ≫ 1 are often misinterpreted as biomass burning aerosol, it was observed that the AAE of purely black carbon particles can be ≫ 1 in the case of larger BC particles. The values of the absorption enhancement factor (E_λ) via coating were found to be between 1.01 and 3.28 in the visible spectrum. The E_λ was derived from Mie calculations for coated volume equivalent spheres and from MSTM for coated BCFAs. Mie-calculated enhancement factors were found to be larger by a factor of 1.1 to 1.5 than their corresponding values calculated from the MSTM method. It is shown that radiative forcings are highly sensitive to modifications in morphology and composition. The black carbon radiative forcing ΔF_TOA (W m⁻²) decreases up to 61 % as the BCFA becomes more compact, indicating that global model calculations should account for changes in morphology. A decrease of more than 50 % in ΔF_TOA was observed as the organic content of the particle increased up to 90 %. The changes in the ageing factors (composition and morphology) in tandem result in an overall decrease in the ΔF_TOA. A parameterization scheme for optical properties of BC fractal aggregates was developed, which is applicable for modelling, ambient, and laboratory-based BC studies. The parameterization scheme for the cross sections (extinction, absorption, and scattering), single-scattering albedo (SSA), and asymmetry parameter (g) of pure and coated BCFAs as a function of D_mob were derived from tabulated results of the MSTM method. Spanning an extensive parameter space, the developed parameterization scheme showed promisingly high accuracy up to 98 % for the cross sections, 97 % for single-scattering albedos (SSAs), and 82 % for the asymmetry parameter (g).