Research about sleep is an attractive topic with scientists. Sleep studies focus on the evaluation of sleep latency, sleep depth, wake-up time, and so on. This study evaluates sleep depth from aperiodic components. Two values are used including exponent and offset. The exponent refers to the rate at which the power spectral density (PSD) decreases with velocity, whereas the offset represents the change in PSD associated with an increase in frequency. This study has used data from the Openneuro Database. Electroencephalogram (EEG) data collected from section naps spent 15 min of 33 participants. The exponent and offset values for each epoch are computed for 30 channels and arranged with 3 labels of sleep stages: W, N1, and N2 of 30 channels. Stage W goes from N1 to N2, the exponent and offset tend to increase. The frontal region of the brain has a mean value of a slope higher than the occiput region of the brain and the slope highest located in the frontal region. Most of the high-energy periodic frequency components are eliminated and fall within the 4–10 Hz, tending to shift towards the 10–15 Hz as the transition from stage W to N2 progresses. The research aligns with previous research when analyzing aperiodic components in naps. Furthermore, it also supports the hypothesis that deeper sleep is associated with steeper slopes, with the steepest slopes located in the frontal brain region, specifically the prefrontal cortex.