<p>The mixing state of black carbon (BC) aerosols can be measured by the single-particle soot photometer (SP2). However, the measured mixing state contains errors, because the core-shell model and Mie scattering calculation are employed in the measurement principle of SP2, and the spherical core-shell structure seriously deviated the real morphology of coated BC. In this study, fractal models are constructed to represent thinly and heavily coated BC particles for optical simulations, the scattering cross-section are selected as reference to conduct optical retrieval of particle diameter (<em>D<sub>p</sub></em>) based on Mie theory, just like the measurement principle of SP2, and the diameter of BC core (<em>D<sub>c</sub></em>) are the same for fractal and spherical models. Then, the measurement errors of mixing state (<em>D<sub>p </sub></em>/ <em>D<sub>c</sub></em>) of BC are investigated from numerical aspect, and the estimation accuracy of BC radiative forcing is analyzed through the simple forcing efficiency (SFE) equation with SP2 measurement results taken into consideration. Results show that SP2 measured <em>D<sub>p </sub></em>/ <em>D<sub>c</sub></em> based on Mie theory underestimates the realistic mixing state of coated BC for most particle sizes, and the largest relative error for single-particle can be about 42 %. The retrieval errors of mixing state of thinly coated BC for both single-particle and particle groups are larger than these of heavily coated BC. In addition, evaluation errors of radiative forcing of coated BC caused by measurement errors of SP2 are up to about 76 % and 43 % at 1064 and 532 nm, respectively. This study provides meaningful referential understandings of the measured <em>D<sub>p </sub></em>/ <em>D<sub>c</sub></em> of SP2.</p>