SHEPHERD, Circuit Judge.

Tony Ray Ferguson appeals from his sentence of 60 months imprisonment imposed after his conviction for possession of a prohibited object in prison. See 18 U.S.C. § 1791(a)(2). He contends that the district court committed multiple procedural errors, abused its discretion by imposing a sentence 48 months above his Sentencing Guidelines range, and violated the Eighth Amendment in imposing a 60 month sentence for a minor possession conviction. We affirm.

I.

Since April 2006, Ferguson has been a federal prisoner at the Federal Correctional Complex in Forrest City, Arkansas ("FCC-Forrest City"). On February 22, 2009, prison staff observed Ferguson remove something from his pocket while he was waiting to leave the visitation room. When the prison staff approached Ferguson, he dropped two bundles onto the ground. One bundle contained 12 grams of marijuana, and the other contained 16 grams of tobacco. Ferguson pled guilty to a one-count indictment for possession of a prohibited object while in prison, in violation of 18 U.S.C. § 1791(a)(2).

At the sentencing hearing, the district court determined that Ferguson had an advisory Sentencing Guidelines range of 6 to 12 months imprisonment. The district court then heard testimony from Agent Eric Thompson, a government witness and a special investigative agent with the Federal Bureau of Prisons at FCC-Forrest City. Agent Thompson testified that possession of contraband was a serious problem at FCC-Forrest City. However, because the quantities possessed were generally small, possession had traditionally been punished internally with little deterrent effect. Agent Thompson had asked the United States Attorney to begin prosecuting possession of contraband, and he noted that the resulting federal indictments had produced a drop in contraband possession. Agent Thompson also stated that of these recent indictments, Ferguson's was the first drug case to proceed to sentencing. Because Ferguson was the first person sentenced during the new enforcement efforts, the government asked the district court to use his sentence to "send a loud, clear message."

The district court accepted the government's argument that Ferguson's sentence had heightened deterrent value. It stated:

[T]his is the test case. Now, it's a terrible thing to be made to be the example. Mr. Ferguson, it's terrible. It's terrible to be the Gilbert Arenas, he was the basketball player for the Washington Wizards who had guns in the locker room just recently, so he's been suspended without pay. He had a 110-million-dollar contract that's going to be void because he had a gun.

It's terrible to be the Michael Vick who fights dogs and they decide to make an example out of him. It's terrible. But this is the first case, and it's just unfortunate for you. Mr. Ferguson, I'm going to commit you to the Bureau of Prisons for 60 months. I'm going to max you out. If they would allow me to give you 20 years, I'd give you 20. This is a very, very, very serious problem in our prisons. I once had a man tell me who I represented, you can get anything in prison you want that you can get outside. We do it all in there. So coming out of the Eastern District of Arkansas, we're going to send a loud and clear message that contraband in prison is not acceptable.

Following this pronouncement, the district court sentenced Ferguson to 60 months imprisonment. Ferguson timely appealed his sentence, raising procedural error, substantive reasonableness, and Eighth Amendment issues.

II.

Ferguson argues that the district court committed three procedural errors: (1) it failed to adequately explain whether it was imposing an upward departure or an upward variance; (2) it failed to consider all of the statutory sentencing factors; and (3) it relied on erroneous fact finding. Because Ferguson did not raise his procedural objections at sentencing, we review for plain error. United States v. McCraney, 612 F.3d 1057, 1067 (8th Cir. 2010).

First, Ferguson argues that the district court committed procedural error in failing to specify whether it was imposing an upward departure under the Guidelines or an upward variance under 18 U.S.C. § 3553(a). He reasons that in the face of this uncertainty, we must remand because a departure requires specific procedural steps and additional explanation. See United States Sentencing Commission, Guidelines Manual, § 4A1.3(a)(4)(B). There is no indication, however, that the district court departed. For example, the district court did not mention a Guidelines departure provision, revisit its Guidelines range calculation as required for a departure, or claim to be departing. Furthermore, although the district court never expressly mentioned section 3553(a), the factors discussed by the district court — the nature and circumstances of the crime, the history and characteristics of the defendant, and the need for general deterrence — are the standard considerations for a variance under section 3553(a), not a departure under the Sentencing Guidelines. Compare 18 U.S.C. § 3553(a), with U.S.S.G. § 4A1.3. Accordingly, we conclude that the district court imposed an upward variance and thus was not required to follow the procedural requirements for departing. United States v. Washington, 515 F.3d 861, 866 (8th Cir. 2008) (concluding that an upward deviation was a variance based on the record).

Second, Ferguson argues that the district court failed to consider all of the section 3553(a) factors by not considering the need to avoid unwarranted sentence disparities. Contrary to Ferguson's contention, "[i]f a district court references some of the considerations contained in § 3553(a), we are ordinarily satisfied that the district court was aware of the entire contents of the relevant statute." United States v. Gray, 533 F.3d 942, 944 (8th Cir. 2008) (quotation omitted). We presume that "district judges know the law and understand their obligation to consider all of the § 3553(a) factors." Id. at 943 (quotation omitted). The district court engaged in an analysis of several section 3553(a) factors, including the nature and circumstances of the offense, Ferguson's history and characteristics, and the need for general deterrence. The court discussed how the offense involved Ferguson's two minor children, Ferguson's extensive criminal history and multiple drug offenses, and the serious problem of drugs in prison and the need to deter other prisoners. We conclude that there was no plain error in the procedural adequacy of the court's consideration.

Third, Ferguson argues that the district court committed procedural error by relying on clearly erroneous factual findings. He says that the district court's conclusion that only a statutory maximum sentence would create a sufficient deterrent effect ignored Agent Thompson's testimony that federal indictments alone have caused a drop in contraband at FCC-Forrest City. Agent Thompson's testimony, however, is not contrary to the district court's conclusion. A severe sentence in a bellwether case would tend to increase the deterrent effect of the indictments. If anything, responsiveness of the inmates to federal indictments would suggest the efficacy of the district court's decision to use a lengthy sentence to send a message. In any event, the district court's deterrence findings are not clearly erroneous.

III.

Ferguson next argues that the district court substantively erred in determining that the section 3553(a) factors supported a sentence of 60 months and justified such a substantial upward variance. At oral argument, Ferguson's counsel emphasized that the upward variance was a 500% increase from the top of Ferguson's Guidelines range.

We review the substantive reasonableness of a sentence under an abuse-of-discretion standard. Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). Although we may consider the extent of the district court's variance, we "give due deference to the district court's decision that the § 3553(a) factors, on a whole, justify the extent of the variance." Id. A sentencing court abuses its discretion when it "fails to consider a relevant factor that should have received significant weight, gives significant weight to an improper or irrelevant factor, or considers only the appropriate factors but commits a clear error of judgment in weighing those factors." United States v. Moore, 565 F.3d 435, 438 (8th Cir. 2009).

The extent of the percentage increase in this case is unremarkable. Gall specifically rejected using "the percentage of a departure as the standard for determining the strength of the justifications required for a specific sentence." Gall, 552 U.S. at 47, 128 S.Ct. 586. The Court warned that when applying a mathematical approach, "deviations from the Guidelines range will always appear more extreme — in percentage terms — when the range itself is low." Id. at 47-48, 128 S.Ct. 586. We have routinely upheld larger absolute month variances, see, e.g., United States v. Larrabee, 436 F.3d 890, 894 (8th Cir. 2006) (affirming upward variance of 128 months), and have upheld larger percentage variances, see, e.g., United States v. Clay, 579 F.3d 919, 934 (8th Cir. 2009) (affirming upward variance of 615%).

Ferguson responds that this case is unique because the district judge justified his sentence primarily by the need to send the message that contraband will not be tolerated in prisons. Ferguson argues it is unfair that his sentence was driven by his misfortune in being the first drug case from FCC-Forrest City to proceed to sentencing, rather than by a consideration of individual factors. However, we have upheld severe sentences imposed in part for reasons unrelated to the personal characteristics of the particular defendant. United States v. Foy, 617 F.3d 1029, 1037 (8th Cir. 2010) (affirming upward variance even though the district court acknowledged a history of "being harder on violent defenders [sic] than what the government often recommends" and for giving defendants with Foy's criminal history a "very bad day") (alteration in original). Furthermore, Congress specifically made general deterrence an appropriate consideration under section 3553(a)(2)(B), and we have described it as "one of the key purposes of sentencing." United States v. Medearis, 451 F.3d 918, 920 (8th Cir. 2006). Finally, other circuits have upheld sentences where district courts indicated a desire to send a message. See, e.g., United States v. Carreto, 583 F.3d 152, 159-60 (2d Cir. 2009); United States v. Blackston, 940 F.2d 877, 894 (3d Cir. 1991); United States v. Malik, 680 F.2d 1162, 1166 (7th Cir. 1982).

In the circumstances of this case, the need for deterrence was a valid sentencing consideration. Ferguson pled guilty to bringing 28 grams of marijuana and tobacco into a prison that Agent Thompson characterized as struggling to gain control of its contraband problem. Agent Thompson also testified that this was the first drug case to proceed to sentencing and that federal prosecutions were having a deterrent effect on the inmates.

Additionally, as described previously, the district court considered all of the section 3553(a) sentencing factors before imposing the upward variance. The district court emphasized that Ferguson's offense was particularly egregious because his minor children were present and Ferguson's criminal history was lengthy, including multiple gun and drug convictions and a state conviction for possession of contraband in a penal institution. Furthermore, the district court had information that Ferguson's extensive disciplinary history at FCC-Forrest City included using drugs and possessing homemade intoxicants, violations not included in his criminal history points. In summary, although some might argue that there is a degree of unfairness when non-personal characteristics contribute to a sentence, here the district court's focus on deterrence and its balancing of the section 3553(a) factors do not make the sentence unreasonable.

IV.

Finally, Ferguson argues that 60 months imprisonment for possession of 28 grams of contraband constitutes cruel and unusual punishment in violation of the Eighth Amendment. We review de novo an Eighth Amendment challenge to a sentence. United States v. Wiest, 596 F.3d 906, 911 (8th Cir. 2010).

The Eighth Amendment "contains a narrow proportionality principle that applies to noncapital sentences." Id. (internal quotations omitted) (quoting Ewing v. California, 538 U.S. 11, 20, 123 S.Ct. 1179, 155 L.Ed.2d 108 (2003)). "[I]t is exceedingly rare for a non-capital sentence falling within the authorized statutory range to constitute a violation of the Eighth Amendment." United States v. Paton, 535 F.3d 829, 838 (8th Cir. 2008). In deciding whether a sentence is grossly disproportionate to a crime, we "compare the gravity of the offense committed to the harshness of the penalty imposed." Henderson v. Norris, 258 F.3d 706, 709 (8th Cir. 2001). Given the serious contraband issues at FCC-Forrest City and Ferguson's extensive criminal history, including several prison contraband violations, we find no gross disparity between the sentence and the crime. Accordingly, we conclude Ferguson's sentence does not violate the Eighth Amendment's prohibition against cruel and unusual punishment.

V.

The judgment of the district court is affirmed.