For granular media, the cluster size is closely related to the grain size and, at the same time, strongly affected by the intergranular exchange coupling strength. We develop the minimum-width detection scheme to analyze the magnetic cluster size and cluster size distribution for perpendicular media. We observed that the median magnetic cluster size strongly depends on the intergranular exchange interaction strength. For the exchange decoupled sample, the magnetic cluster size is close to the grain size of 7.6 nm. With increasing magnitude of the exchange interaction, the cluster size increases to about 19 nm for H-ex=10 kOe. Similar to the median cluster size, the standard deviation of the magnetic cluster size also increases with increasing exchange interaction strength. However, the fractional standard deviation of the cluster size, defined as the ratio between the distribution and the median cluster size, shows little dependency on the intergranular exchange interaction strength. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3001804]