KRAVITCH, Circuit Judge:
The survivors of a man killed in a police shootout in DeKalb Counly, Georgia brought this action pursuant to 42 U.S.C. § 1983 against the officers involved in the shootout, certain county officials, and the County. The district court granted the defendants’ motion for summary judgment on the ground that the decedent’s constitutional rights had not been violated and therefore no section 1983 action could be maintained, 667 F.Supp. 853. We affirm.
I.
On the evening of December 15, 1983, the decedent, George Washington O’Neal, Sr., a patient at Doctor’s Hospital in De-Kalb County, Georgia, went on a rampage through the hospital and stabbed seven people with a pocketknife. Officer Steven Waits, a DeKalb County police officer, arrived at the hospital in response to a police call. Waits, armed with his service revolver, found O’Neal on the second floor, holding a bloody knife. Waits identified himself as a police officer and ordered O’Neal to drop his knife. Ignoring Waits’s demand, O’Neal ran away down the hallway. As Waits chased O’Neal through the second floor corridors, he observed “a lot of blood on the floor ... a piece of intral [sic] of some kind” and a person with a severe stomach wound lying on the floor. Deposition of Steven W. Waits, at 54. He also noticed that the nursing supervisor had a stab wound in his back. Police Report, Plaintiffs Exhibit 2.
After Waits had chased O’Neal for approximately five minutes, Officer Rick Ro-seberry, armed with a shotgun, arrived at the hospital to assist Waits. Roseberry also saw “blood all over the floor” and walls and “a piece of human tissue lying there in [sic] the floor in front of me.” Deposition of Rickie Emmit Roseberry, at 66. Soon after Roseberry’s arrival, the two officers cornered O’Neal at the end of one of the second floor corridors so that O’Neal was standing only six feet from Roseberry and between five and six feet from Waits. With their weapons raised, the officers repeatedly ordered O’Neal to drop his knife and lie on the floor. Instead of complying, O’Neal rushed toward Rose-berry with the knife raised over his head; in response, both officers fired their weapons at O’Neal. Although struck by both shots, O’Neal did not fall, but rather twisted around from the force of the shots, still waving his knife above his head. Immediately after the first volley of shots, Rose-berry fired a second shot, which hit O’Neal in the small of the back and brought him to the ground. O’Neal died as a result of the gunshot wounds.
O’Neal’s survivors brought this section 1983 action against Waits, Roseberry, the Director of Public Safety of DeKalb County, the Chief of Police and Assistant Chief of Police of DeKalb County, and DeKalb County. The complaint alleged that Waits and Roseberry had deprived O’Neal of his constitutional rights by using excessive force against him, and that this use of excessive force was the result of a custom or policy of DeKalb County. Concluding that O’Neal’s constitutional rights had not been violated because the officers had not used excessive force, the district court granted summary judgment for all the defendants. In a separate order, the district court denied the defendants’ motion for attorney’s fees under 42 U.S.C. § 1988 and Federal Rule of Civil Procedure 11. The plaintiffs appeal, arguing that the district court erred in granting summary judgment on the issue of excessive force. The defendants cross-appeal from the denial of attorney’s fees.
II.
To succeed on their section 1983 claim, the plaintiffs must establish that O’Neal was deprived of a constitutional right. Baker v. McCollan, 443 U.S. 137, 138, 99 S.Ct. 2689, 2692, 61 L.Ed.2d 433 (1979); Shillingford v. Holmes, 634 F.2d 263, 265 (5th Cir. Unit A 1981). The plaintiffs advance two plausible constitutional theories to support their section 1983 action; they assert that the officers’ use of force against O’Neal violated his right to substantive due process and his rights under the fourth amendment. We will consider these assertions separately. See Gilmere v. City of Atlanta, 774 F.2d 1495, 1499 (11th Cir.1985) (en banc) (analyzing claim of excessive force under both substantive due process and fourth amendment), cert. denied, 476 U.S. 1115, 106 S.Ct. 1970, 90 L.Ed.2d 654 (1986).
A. Substantive Due Process
The starting point for any discussion of a substantive due process claim in the context of police abuse is Rochin v. California, 342 U.S. 165, 72 S.Ct. 205, 96 L.Ed. 183 (1952), in which the Supreme Court held that incriminating evidence obtained by subjecting a criminal suspect to a stomach pump was inadmissible. As the Court explained, substantive due process is violated when the government engages in actions that “ ‘offend those canons of decency and fairness which express the notions of English-speaking peoples even toward those charged with the most heinous offenses.’ ” Id. at 169, 72 S.Ct. at 208 (quoting Malinski v. New York, 324 U.S. 401, 416-17, 65 S.Ct. 781, 788-89, 89 L.Ed. 1029 (1945)). In other words, government conduct that “shocks the conscience,” id. at 172, 72 S.Ct. at 209, or “offend[s] even hardened sensibilities,” id., 72 S.Ct. at 210, transgresses the bounds of substantive due process.
Since Rochin, the lower courts have developed more definite standards for identifying substantive due process violations. In determining whether force used by police officers amounts to a constitutional deprivation, a court must consider “‘the need for the application of force, the relationship between the need and the amount of force that was used, the extent of the injury inflicted, and whether force was applied in a good faith effort to maintain or restore discipline or maliciously and sadistically for the very purpose of causing harm.’” Gilmere v. City of Atlanta, 774 F.2d 1495, 1500-01 (11th Cir.1985) (en banc) (quoting Johnson v. Glick, 481 F.2d 1028, 1033 (2d Cir.), cert. denied, 414 U.S. 1033, 94 S.Ct. 462, 38 L.Ed.2d 324 (1973)), cert. denied, 476 U.S. 1115, 106 S.Ct. 1970, 90 L.Ed.2d 654 (1986).
The plaintiffs’ substantive due process argument is two-tiered. First, they maintain that the use of gunfire against a suspect armed only with a knife was constitutionally excessive because less harmful methods of apprehension were available. Second, they argue that assuming the first volley of gunfire was constitutional, Rose-berry’s second shot was not. We reject both parts of the plaintiffs’ argument.
Unquestionably, the situation at Doctor’s Hospital on the evening of December 15, 1983 suggested the need for the application of force. O’Neal had just stabbed several people and, at the time he was shot, was charging at Roseberry with his knife raised over his head. He refused to respond to the officers’ demands that he surrender, leaving them with the definite impression that force was required to stop him from hurting Roseberry or someone else. Moreover, the amount of force used did not exceed the need for the use of force. The plaintiffs maintain that O’Neal’s rights were violated because the officers could have disarmed him by negotiating with him or by using a baton or stungun, instead of resorting to gunfire. However, they point to no authority holding that the Constitution requires police officers to use a minimum of force to apprehend a violent, dangerous suspect who is threatening the lives of the officers and others nearby. In this case, the use of gunfire to disarm O’Neal was not excessive in light of the obvious danger he posed to the lives of others. In addition, the undisputed evidence demonstrates that the officers fired their guns in a good faith effort to stop O’Neal, not out of a malicious desire to cause harm. Although the injury inflicted was the worst possible, death, the result of the use of force is but one factor to be considered in determining if such force was excessive. Despite the tragic outcome of Waits’s and Roseberry’s encounter with O’Neal, we remain convinced that they did not use excessive force in attempting to subdue him. In short, then-reaction to O’Neal’s violent behavior does not “shockQ the conscience” or “offend ... hardened sensibilities.” Rochin, 342 U.S. at 172, 72 S.Ct. at 209-10.
Our opinion does not change because Roseberry fired a second shot at O’Neal. As the plaintiffs admitted in their brief and at oral argument, Roseberry fired his second shot “immediately” after his first, and at the time of the second shot, O’Neal was still on his feet, holding his knife and spinning from the force of the first volley of shots. These undisputed facts convince us that Roseberry’s second shot was part of his initial reaction to O’Neal’s attempt to stab him, and not, as the plaintiffs would have us believe, a brutal, gratuitous use of force against a visibly disabled suspect. Viewed as part of his initial reaction to O’Neal’s attack, and in light of the unusual circumstances facing the officers that evening, Roseberry’s firing of two shots in rapid succession in an attempt to guarantee O’Neal’s apprehension did not constitute excessive force.
B. The Fourth Amendment
The plaintiffs also base their section 1983 action on the fourth amendment, which provides in pertinent part that “[t]he right of the people to be secure in then-persons ... against unreasonable searches and seizures shall not be violated.” As the Court recently noted in Tennessee v. Garner, 471 U.S. 1, 105 S.Ct. 1694, 85 L.Ed.2d 1 (1985), “there can be no question that apprehension by the use of deadly force is a seizure subject to the reasonableness requirement of the Fourth Amendment.” Id. at 7, 105 S.Ct. at 1699. Reasonableness is determined by “ ‘balancing] the nature and quality of the intrusion on the individual’s Fourth Amendment interests against the importance of the governmental interests alleged to justify the intrusion.’ ” Id. at 8, 105 S.Ct. at 1699 (quoting United States v. Place, 462 U.S. 696, 703, 103 S.Ct. 2637, 2642, 77 L.Ed.2d 110 (1983)).
Under this balancing test, the plaintiffs’ fourth amendment claim must fail. Although O’Neal’s “fundamental interest in his own life need not be elaborated upon,” id. at 9, 105 S.Ct. at 1700, even such a weighty interest may be counterbalanced by governmental interests in effective law enforcement, as in this case. Waits and Roseberry used deadly force to protect themselves and the people at the hospital from O’Neal, who was armed and, as the blood-covered floors and injured bodies demonstrated, extremely dangerous. Considering the trying circumstances that the officers faced, their reaction, including Ro-seberry’s second shot, was reasonable and hence within the bounds of the fourth amendment.
III.
On cross-appeal, the defendants argue that the district court abused its discretion in not granting them attorney’s fees under 42 U.S.C. § 1988 or Federal Rule of Civil Procedure 11. Pursuant to section 1988, a district court may award attorney’s fees to prevailing defendants if “ ‘the plaintiff’s action was frivolous, unreasonable, or without foundation, even though not brought in subjective bad faith.’ ” Hughes v. Rowe, 449 U.S. 5, 14, 101 S.Ct. 173, 178, 66 L.Ed.2d 163 (1980) (quoting Christiansburg Garment Co. v. EEOC, 434 U.S. 412, 421, 98 S.Ct. 694, 700, 54 L.Ed.2d 648 (1978)). “The fact that a plaintiff may ultimately lose his case is not in itself a sufficient justification for the assessment of fees.” Id., 101 S.Ct. at 178. Similarly, a court may require a party or its counsel to pay reasonable attorney’s fees to the prevailing party pursuant to Federal Rule of Civil Procedure 11 as a sanction for filing an action that has no factual or legal foundation. See Donaldson v. Clark, 819 F.2d 1551, 1555-56 (11th Cir.1987) (en banc).
Simply because the district court granted the defendants’ motion for summary judgment does not mean that the plaintiffs’ action was frivolous. As the district court pointed out in its order denying fees, in ruling on the motion for summary judgment, it “reviewed a great deal of caselaw [sic] on the issue of when deadly force constitutes unreasonable and excessive force within the meaning of the Constitution,” and “did not find any case with a fact situation similar to the one at hand.” We agree with the district court that although the plaintiffs’ section 1983 suit does not merit relief, their causes of action were plausible. Given this, we cannot say that the district court abused its discretion in denying attorney fees under section 1988 or Rule 11. Cf. Hughes v. Rowe, 449 U.S. at 15, 101 S.Ct. at 179 (allegations properly dismissed for failure to state a claim deserved and received careful attention of the courts and thus were not groundless or without foundation).
For the foregoing reasons, the judgment of the district court is AFFIRMED.
. The plaintiffs claim that O’Neal’s outburst was caused by medication he was given while a patient at the hospital.
. The complaint also asserted pendent state claims against Roseberry and Waits for wrongful death and against Doctor’s Hospital for wrongful death and medical malpractice. Upon granting summary judgment for the defendants, the district court dismissed the pendent claims without prejudice.
. In pertinent part, 42 U.S.C. § 1983 provides as follows:
Every person who, under color of any statute, ordinance, regulation, custom or usage, of any State ... subjects, or causes to be subjected, any citizen of the United States ... to the deprivation of any rights, privileges, or immunities secured by the Constitution and laws, shall be liable to the party injured in an action at law.
.The complaint alleged that the defendants had violated O’Neal’s rights "to life, equal protection of the laws, and freedom from cruel and unusual punishment under the Fifth, Eighth and Fourteenth Amendments to the United States Constitution." The district court noted that “[i]n response to defendants’ motion for summary judgment, plaintiffs appear to assert that O’Neal’s life was unreasonably seized in violation of the Fourth Amendment." Accordingly, the district court analyzed the plaintiffs’ claim under the fourth amendment, even though it was not mentioned in their complaint. In their briefs to this court, the plaintiffs continue to argue that O’Neal’s rights under the fourth amendment were violated. Thus, we will also proceed on the assumption that the plaintiffs’ claim is brought under both the fourth and fourteenth amendments.
As for the remaining constitutional claims asserted in their complaint, the plaintiffs concede that their eighth amendment claim must fail as a matter of law; their equal protection claim is also groundless and does not merit discussion.
. The plaintiffs stress that Roseberry’s second shot hit O’Neal in the back, as if this conclusively demonstrates that this shot was fired "maliciously and sadistically for the very purpose of causing harm.” Gilmere, 774 F.2d at 1501. As the plaintiffs admit, however, Roseberry fired his second shot “immediately" after his first. At the time Roseberry fired his second shot he could not have known that O’Neal would twist around from the force of the first round of shots and consequently be hit in the back by the second shot. Ilius, the fact that Roseberry’s second shot hit O’Neal in the back does not transform Rosebenys conduct into a violation of substantive due process.
. The dissent maintains that summary judgment was improper because there is a conflict in the record regarding the proportionality of the force used, and "such conflict is for the ultimate fact finder, not this court, to resolve and then weigh against the fact that O’Neal lost his life.” The dissent, however, seems to confuse the process of finding historical facts, a function of the jury, with the distinct process of determining whether those historical facts constitute a substantive due process or fourth amendment violation, a function of the court. See Gilmere, 774 F.2d at 1500-01 (court must determine whether there was substantive due process violation by looking to four factors); Tennessee v. Garner, 471 U.S. 1, 8, 105 S.Ct. 1694, 1699, 85 L.Ed.2d 1 (1985) (reasonableness under fourth amendment is question of law). The proportionality of the force used, the focus of the second prong of the Gilmere due process test and a factor in determining reasonableness under the fourth amendment, is for the court, not the jury, to consider. In a case such as this, where the historical facts are undisputed, it is this court's duty to decide, as a matter of law, whether the facts support the appellants’ constitutional claim.
. Citing Gamer, the plaintiffs argue that the officers violated O’Neal’s fourth amendment rights because they shot at him although he was not trying to escape. The passage from Gamer that the plaintiffs rely upon states as follows:
[I]f the suspect threatens the officer with a weapon or there is probable cause to believe that he has committed a crime involving the infliction or threatened infliction of serious physical harm, deadly force may be used if necessary to prevent escape, and if, where feasible, some warning has been given.
471 U.S. at 11-12, 105 S.Ct. at 1701.
We are not persuaded by this argument. Initially, we take issue with the plaintiffs’ underlying factual assumption that O’Neal was not trying to escape when he was shot. O'Neal’s attempt to stab Roseberry could very well be interpreted as an attempt to escape from the officers and continue his rampage through the hospital. Next, we note that the plaintiffs have misread Gamer to hold that a police officer can no longer use deadly force to defend himself against a suspect’s use of deadly force, unless the suspect is also trying to escape. A more sensible interpretation of the above quoted passage is that a police officer may, under certain circumstances, use deadly force to prevent the escape of a suspect; it does not mean that the use of deadly force is limited to those instances where a suspect is trying to escape.