How much money does it take to pay each service member in the US military per pay period?

In FY24, total military payroll was about $14,7B per month. But that does include BAS, BAH, and special and incentive pays and bonuses.
1.33M service members were active duty, including AGRs for the Guard and Reserve, and about 800K in the Guard either on a drill status or on orders of some kind.

2LT(P) (Join to see), if you REALLY want to get a breakdown, you can get all the raw info from the Department's Comptroller*. FY26's base budget request has the actual expenditures for FY24 in them (there are over 60 different 'personnel' budget sub activities that are used).

However, a quick and dirty extraction of the info for how much the Department spent for all Services in FY2024 was:
• Basic Pay: $67.63B (~$5.64B/month)
• BAS: $5.26B (~$0.44B/month)
• BAH: $25.73B (~$2.14B/month)

To get a more accurate figure, you'd have to add in everything else that goes along with base pay ... SS/Medicare tax the employer pays ($5.16B), TSP matching contributions ($1.29B), etc.

As SGM Jeff Mccloud stated, the entire budget expenditures were about $14.7B per month, but it also includes things you probably would never think to account for if you didn't have the documents in front of you.
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* https://comptroller.war.gov/Portals/45/Documents/defbudget/FY2026/m1_display.xlsx

You’d basically have to factor in every pay grade from E-1 all the way up to O-10, multiply by headcount in each rank, and then apply time in service brackets. And even then, the number shifts constantly because people are enlisting, ETSing, promoting, separating, etc. The DoD publishes the annual military payroll in the budget docs, though, and if you break it down by 24 pay periods, you're easily talking billions per pay period. Base pay alone for the active component is already enormous before even touching BAH or benefits.