[en] Highlights: • Real and imaginary parts of optical conductance separately are calculated. • Absorption coefficient in monolayer circular graphene quantum dots is calculated. • Absorption coefficient in bilayer circular graphene quantum dots is calculated. • Comparing between Absorption coefficient of mono and bilayer circular graphene quantum dots was done. • Effect of external magnetic and electric filed on absorption coefficient is investigated. We present an analytical method to calculate photon absorption coefficient in mono and bilayer circular graphene quantum dots (CGQDs). We use kobo equation to extract new closed relation as the main goal. First, we calculate real and imaginary part of optical conductance separately. Then, joint density of states is obtained using a new relation that was extracted for the energy levels of mono and bilayer circular grapheme quantum dots. In this work we use closed equations to calculate energy levels in CGQDs. Next we obtain a new closed formula to calculate the photon absorption coefficient. The results show that the absorption coefficient is related to the size of CGQDs and number of layers. The photon absorption coefficient becomes lower with larger size of CGQDs. It is seen that the results of our method is compatible with the results of practical works. We also compare photon absorption in biased and unbiased bilayer CGQDs and investigate the effect of external magnetic field on photon absorption. © 2001 Elsevier Science. All rights reserved