Free Diapers For Low Income Families – Believe it or not, diapers can be one of the biggest expenses for low income families. Here’s some math to consider: a newborn baby requires around 60 diapers in a week. A pack of diapers can cost about $15, which means that the cost of each diaper is around 30 cents. That means in a month you’ll be spending around $60 to $72 for diapers alone. That is a lot of money for people from low income families.