John Calvin Commentary Romans 13:4

"for he is a minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is a minister of God, an avenger for wrath to him that doeth evil." — Romans 13:4 (ASV)

For he is God’s minister for good, etc. From this, magistrates may learn what their calling is, for they are not to rule for their own interest, but for the public good; nor are they endowed with unbridled power, but rather with power restricted to the well-being of their subjects. In short, they are responsible to God and to men in the exercise of their power. For as they are appointed by God and do His work, they must give an account to Him: and the ministry which God has committed to them concerns the subjects; they are therefore also debtors to them. And private citizens are reminded that it is through divine goodness that they are defended by the sword of rulers against harm done by the wicked.

For they bear not the sword in vain, etc. It is another part of the office of magistrates to forcibly repress the rebelliousness of evil men, who are unwilling to be governed by laws, and to inflict such punishment for their offenses as God’s judgment requires; for Scripture expressly declares that they are armed with the sword, not for an empty show, but so that they may strike evil-doers.

And then Scripture says, An avenger, to execute wrath, etc. This is the same as saying that the magistrate is an executioner of God’s wrath; and he shows himself to be this by bearing the sword, which the Lord has delivered into his hand. This is a remarkable passage for proving the right of the sword; for if the Lord, by arming the magistrate, has also committed to him the use of the sword, whenever he punishes the guilty with death, he obeys God’s commands by executing His vengeance. Then do those contend with God who think it unlawful to shed the blood of wicked men.