Sinners cannot keep the law of God perfectly, and this is why the law's promise of justification for those who keep it can never be fulfilled by our own obedience (Rom. 10:5; see Gal. 3:10-14). Justification, therefore, must be by faith alone, a faith that looks outside of oneself to the promises of the Lord and not to any goodness we can achieve even with His help. Justification by faith alone acknowledges that we are no more deserving of salvation than any other sinner, and it recognizes that God alone must do the work of salvation (Rom. 10:6-8). Yet this does not mean that the righteousness based on faith is entirely removed from the law of God. In fact, the righteousness by faith is a righteousness that comes from keeping the Lord's commandments perfectly, although it is not we who have kept them. The One who has kept them is Christ Jesus our Lord, who obeyed the law perfectly unto the justification of sinners (1 Peter 2:20-23; see Rom. 5:12-21). The righteousness that is by faith is indeed a legal righteousness, but we have not achieved it. It has been achieved by Christ, and it is imputed to us when we trust in Him alone (2 Cor. 5:21).
In Romans 10:9-13, Paul continues his argument that the righteousness that is by faith— which is nothing less than Christ, the end or goal of the law—is antithetical to the righteousness that is based on keeping the law. He does this by emphasizing the ease with which this righteousness of our Savior is received. All that is required is belief—specifically, the belief in the heart that God raised Jesus from the dead (vv. 9-10). Of course, Paul in the same verses also mentions the confession of Jesus as Lord with one's mouth, but he does not thereby make verbal confession something that we add to our belief in order to be saved. The Apostle is paralleling the simplicity of the righteousness of faith with the fact that one does not have to go looking high and low for the gospel, for heart and mouth are mentioned in verses 6-8. Paul is stressing the nearness of the gospel message. The message of justification by grace alone through faith alone in Christ alone is not so far away intellectually that one must exert great effort to bridge the gap between present knowledge and "gospel knowledge." It is so easy to understand that it is right at hand even for the unlearned.
Paul wants us to know that righteousness by faith is ours via a gospel that anyone can understand. Everyone who calls on the name of the Lord will be saved (vv. 11-13). Jew or Gentile, learned or unlearned, male or female—the gospel is no respecter of persons.
John Calvin comments on today's passage that the emphasis on believing with the heart shows that "faith is a firm and effectual confidence and not a bare notion only." Saving faith is not simply knowing the truth about Jesus or believing the facts about His life, although these things are necessary. Saving faith also requires personal trust in Jesus for salvation, the belief that His work and promises apply to us specifically. If we believe such things, we are saved.