The standard of righteousness is God, and if we are in Christ, our righteousness is Jesus' own, imputed to us. "That I may gain Christ and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ—the righteousness that comes from God on the basis of faith". Philippians 3:8b-9. Here is a list of worship songs & hymns about righteousness.
