I fully agree with the first answer given. House arrest is usually a function of bail requirements which means the person is released to their home during the pendancy of the case and sentencing only occurs at the end of the case. If the person had stayed in jail while the case was pending, that would be a different story.
Ted and Cynthia are right. However, a judge can consider house arrest when determining the sentence in the case. Once the judge imposes sentence, the Bureau of Prisons determines the length of time that the defendant will be incarcerated. The BOP will give credit for time served in jail prior to sentencing but not time under home confinement. This is imperative that the attorney ask the judge to consider that period in calculating the sentence. Once the sentence is imposed, this period can longer be considered.
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House arrest (known as electronic monitoring or "EM") does not count as credit toward a sentence of incarceration. In the old days while the US Sentencing Guidelines were mandatory, a lawyer was essentially prohibited from even raising the argument to reduce a Guidelines sentence. Even now, if your are charged with an offense for which a mandatory minimum sentence applies, there is no credit. A federal case can take upwards of eighteen months to bring to trial or resolution. Spending that time locked in the house can feel like prison.
My response is merely offered as public discussion of contemporary legal issues and not as lawyer client advice.
PS. Do not confuse Electronic Monitoring on Supervised Release with federal "Pre-Release" under a Bureau of prisons program where the BOP has statutory authority to allow home confinement for the last ten per cent or six months of the sentence, whichever is less. 18 USC 3624.