This study investigates the carrier density landscape of graphene using a scanning single electron transistor (SET). The researchers observed electron-hole puddles, which are expected theoretically when the average carrier density is zero due to the presence of disorder. The local compressibility measurements, which provide insights into the Coulomb interaction, revealed that the kinetic energy term alone quantitatively describes the data, suggesting that exchange and correlation effects are either weak or cancel out. The spatial variations in the Dirac point were mapped, showing density fluctuations on a scale of about 150 nm. These fluctuations were further analyzed using quantum Hall effects, providing a lower bound for the intrinsic disorder amplitude. The results indicate that the intrinsic disorder length scale in graphene is approximately 30 nm, and high carrier density smoothens out the disorder landscape near the neutrality point.This study investigates the carrier density landscape of graphene using a scanning single electron transistor (SET). The researchers observed electron-hole puddles, which are expected theoretically when the average carrier density is zero due to the presence of disorder. The local compressibility measurements, which provide insights into the Coulomb interaction, revealed that the kinetic energy term alone quantitatively describes the data, suggesting that exchange and correlation effects are either weak or cancel out. The spatial variations in the Dirac point were mapped, showing density fluctuations on a scale of about 150 nm. These fluctuations were further analyzed using quantum Hall effects, providing a lower bound for the intrinsic disorder amplitude. The results indicate that the intrinsic disorder length scale in graphene is approximately 30 nm, and high carrier density smoothens out the disorder landscape near the neutrality point.