1 An average size box of diapers will cost between $15 and $25. 2  Because each box usually contains between 60-100 diapers, this price per box translates to a price per diaper (unit price) of $.15-$.40. For the first year, it is estimated that a baby will use an average of 5 diapers per day. 2  This is a total of approximately 1825 diapers, which gives a yearly cost of about $460. 3  When a baby is 2-3 years old, he will only use 3 or 4 diapers a day.