Ben,
Here are the basics.
Basic Allowance for Housing (BAH)
Regular Army: Active Duty
Benefit Fact Sheet
Summary
Basic Allowance for Housing (BAH) is a United States (U.S.) based allowance that provides uniformed Service members equitable housing compensation based on housing costs in local housing markets when government quarters are not provided. A Service member stationed outside the U.S., including U.S. territories and possessions, who does not have government housing available is eligible for Overseas Housing Allowance (OHA).
Several types of BAH satisfy various housing situations that occur among military members. In general, the amount of BAH you receive depends on your location, pay grade, and whether you have dependents. Under most circumstances, you receive BAH for your assigned location, not where you live. Additionally, you may be entitled to some BAH amounts if you reside separately from your dependents. This occurs in situations involving unaccompanied overseas tours or having a dependent Child that resides with a Former Spouse. The rules regarding these situations can become quite complex. Consult your Finance Office if you are in one of these situations.
The BAH rates have increased an average of 12.1%, effective January 1, 2023.
Reference,
United States Army. (2022). Basic Allowance for Housing (BAH). Retrieved from https://myarmybenefits.us.army.mil/Benefit-Library/Federal-Benefits/Basic-Allowance-for-Housing-(BAH)?serv=122