In order to calculate staffing for any of the desired shifts, the starting point is the number of hours that are required for coverage per year. If you have a minimum manning of five person and there are 24 hours in a day and 365 days in a year, there is a base requirement for coverage of 43,800 hours.
The next calculation is to determine how many hours per year (ideally) you will get from each position. A 12-hour shift normally provides 42 hours of work per week or 2,184 hours per year. A typical 8 hour day shift provides 2080 hours per year. Each of those shifts are usually staffed with a four-platoon system. The 24-hour shift with a 56 hour work week (allowable by FLSA) affords 2,912 hours on the job and is normally accomplished with 3 platoons versus 4 for the other staffing models.
Critical to determining the numbers that you will need for staffing without overtime is calculating the hours that are NOT worked. In other words, how many hours will be given off for holidays (if any)? How many hours will be given off for vacation and sick? In this part of the calculation, contracts should specify hours, not days, especially if you are going from an 8 hour shift to a 12 or 24 hour shift. The reason is that if you have awarded leave time in days and convert the days to another time period, you may automatically triple the amount of time off given to your employees. Another pitfall is that employees working 24 hour shifts like to negotiate "Kelley Days." These are days off given in incremental pieces which lower the actual hours worked from 56 per week to something less. The Center for Public Safety Management has reviewed a number of contracts that lower the actual hours worked to 40 per pay period. This becomes a problem because of the 40, half are spent sleeping so actual hours worked may be 20 or less!
Subtracting the hours NOT worked from the total hours scheduled is then divided into the hours that are needed. The result is the staffing required for coverage. Dividing that number by the shifts equals the personnel per shift.
Don't forget -- because 24 hour schedules normally use 3 squads versus four, your overall staffing is reduced. Using the formula given, and allowing 10 vacation day-equivalents for 8, 12, and 24 hour shifts shows that all three need about 5.5 persons per squad to keep a minimum of 5 on duty. But the 8 and 12 scenarios would require a total of 21.2 to 21.8 in overall numbers while the 24 hour shift (without any Kelley days) would require only 16.4 total personnel.