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The Simple Math Behind The Federal Good Time Sentence Calculator

Murwell recently released a "U.S. Federal Prison Good Time Sentence Calculator." The calculator simplifies the Federal Bureau of Prison's method to determine a sentence after deduction of Good Credit Time.

If you've ever read the BOP's Sentence Computation Manual and felt like your head was going to explode, don't feel bad. Albert Einstein wouldn't understand the Bureau of Prison's method to calculate good credit time for a federal sentence.

The GCT formula is based on dividing 54 days (the maximum number of days that can be awarded for one year in service of a sentence) into one day which results in the portion of one day of GCT that may be awarded for one day served on a sentence. 365 days divided into 54 days equals .148. Since .148 is less than one full day, no GCT can be awarded for one day served on the sentence. Two days of service on a sentence equals .296 (2 x .148) or zero days GCT; three days equals .444 (3 x .148) or zero days GCT; four days equals .592 (4 x .148) or zero days GCT; five days equals .74 (5 x .148) or zero days GCT; six days equals .888 (6 x .148) or zero days GCT; and seven days equals 1.036 (7 x .148) or 1 day GCT. The fraction is always dropped.
Since, in accordance with the statute (18 USC § 3624(b)), no GCT can be awarded to a sentence of one year or less, then the very shortest sentence that can be awarded GCT is a sentence of 1 year and 1 day. Because a prisoner would accrue GCT while serving a sentence of 1 year and 1 day and, therefore, serve something less than the full sentence, it would be impossible to accrue the full 54 days of GCT for a sentence of 1 year and 1
day. As a result, the GCT formula previously discussed must be utilized as shown below to determine the amount of GCT to award for a partial year. This method of calculating the GCT possible to award for the last portion of a year of a sentence to be served must be followed in all partial year calculations. (For the purpose of this demonstration, the sentence of 1 year and 1 day equals 366 days.)
Step No. 1
Sentence = 366 - 54 = 312 days
312 days served does not equal 54 days of GCT but does equal 46
days.
Step No. 2
Days Served = 312 x .148 = 46.176 = 46 days GCT
Subtracting 46 days from the sentence of 366 days results in 320
days to be served.
Step No. 3
Sentence = 366 - 46 = 320 days
46 days of GCT is not enough because 46 plus 312 days to be
served equals a sentence of 358 days, 8 days short of a sentence
of 366 days (1 year and 1 day).
Step No. 4
Time Served = 312 + 46 = 358 days
Comparing 320 days to serve, which is too much time to serve,
with 312 days to serve, which is not enough time to serve,
reveals that the amount of GCT that can be earned must fall
somewhere between 54 and 46 days. As a result, the next step is
to determine how much GCT can be earned on 320 days served.
Step No. 5
Time Served = 320 x .148 = 47.36 = 47 days GCT
Subtracting 47 days from the sentence of 366 days (1 year and 1
day)
results in 319 days to be served.
Step No. 6
Sentence = 366 - 47 = 319 days
Utilizing the GCT formula, it is learned that 319 days served
equals
47 days GCT.
Step No. 7
Time Served = 319 x .148 = 47.212 = 47 days GCT
Adding 319 days time served to 47 days GCT does equal a sentence
of 366 days (1 year and 1 day).
Step No. 8
Time Served = 319 + 47 = 366 days
The amount of GCT that can be awarded for a sentence of 366 days
(1 year and 1 day) is 47 days.

Now, if you want to calculate a federal sentence after deducting good time credit, you can either try to reproduce the BOP's mind-numbing procedure or just do the following simple division:

(Days Sentenced to Prison)/419 = Good Time Sentence in Years

This formula should get you pretty close to the BOP's computations.

Example: Sentence is 366 days.

366/419 = Good Time Sentence in years

.8735 years or 319 days is the Good Time Sentence.

And to get the number of "Good Time Credit Days" just use basic subtraction:

Actual Sentence - Good Time Sentence = Good Time Credit days

366 - 319 = Good Time Credit Days

47 = Good Time Credit Days

Reason Days Sentenced to Prison/419 = Good Time Sentence in Years
Works

Congress provided for a 15% deduction for federal sentences of more than a year when "the prisoner has displayed exemplary compliance with institutional disciplinary regulations." 18 USC 3624.

There are usually 365 days in a year.

15% of 365 = 54.75

Dropping the fraction, one winds up with 54.

365 + 54 = 419

So every year, the prisoner is actually receiving credit for 419 days.

Then to figure out the good time sentence, just divide the number of days of the actual sentence by 419 rather than 365.

Example: Ten year sentence

Actual Sentence - Good Time Sentence = Good Time Credit days

10 x 365 = 3650 is the total sentence in days (not including any additional days for leap years).

3650 / 419 = 8.71 years or 8 years, 8.52 months.

This works pretty close to the BOP's numbers. There will be variations due to leap years, rounding, and procedure. But (Days Sentenced to Prison)/419 = Good Time Sentence in Years should get a reasonable estimation.

To save everyone the trouble, there's a Murwell web app that does the work for you. And, as an extra bonus, looks great on a phone or tablet.

You can find the "U.S. Federal Prison Good Time Sentence Calculator" here.

Disclaimer: While it's believed to be accurate, there are no guarantees, warranties, or representations. The application and website does not provide any legal advice. If you are facing a criminal charge, you MUST get a lawyer.