One of the most prominent early residents of Brady Township was Judge William Piatt. Piatt was born and raised in the area that is now Brady Township. His father, John Piatt, moved to the southern part of Lycoming County from New Jersey and established a tannery. William was born on January 29, 1795 and followed his father into the tannery business. He soon took an interest in the local political scene and was elected to the Pennsylvania General Assembly in 1830. He served as a legislator for three terms. Piatt became an associate judge in 1855. Piatt also served Lycoming County and Brady Township as a county auditor and as a president of both a turnpike and a bridge company.
According to the United States Census Bureau, the township has a total area of 8.6 square miles (22.4 km²), all of it land. It is the location of the Lycoming County Landfill and the northern part of the Federal Correctional Institute, Allenwood.
There were 177 households out of which 31.6% had children under the age of 18 living with them, 73.4% were married couples living together, 5.1% had a female householder with no husband present, and 15.8% were non-families. 11.9% of all households were made up of individuals and 5.6% had someone living alone who was 65 years of age or older. The average household size was 2.79 and the average family size was 2.96.
In the township the population was spread out with 24.5% under the age of 18, 5.9% from 18 to 24, 30.2% from 25 to 44, 28.5% from 45 to 64, and 10.9% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 114.8 males. For every 100 females age 18 and over, there were 103.8 males.
The median income for a household in the township was $43,958, and the median income for a family was $45,313. Males had a median income of $30,294 versus $24,531 for females. The per capita income for the township was $17,789. About 2.9% of families and 6.7% of the population were below the poverty line, including 7.3% of those under age 18 and 14.3% of those age 65 or over.