The Reformation doctrine that justification involves two imputations (reckonings): (1) the believer's sin is imputed to Christ (2 Corinthians 5:21a — "he made him to be sin who knew no sin"); (2) Christ's righteousness is imputed to the believer (2 Corinthians 5:21b — "so that in him we might become the righteousness of God"). Martin Luther coined the evocative phrase simul iustus et peccator — "at the same time righteous and a sinner" — to capture the legal reality: the Christian is declared righteous in Christ while still being progressively sanctified in himself.
Double imputation is the Reformation's gospel distilled. Roman Catholic theology affirmed imputation of sin to Christ but taught that the believer is made inherently righteous (infused righteousness) gradually over a lifetime and possibly through purgatory. The Reformers insisted this collapses justification into sanctification and destroys assurance — because you can never know if enough righteousness has been infused. Their answer: your righteousness before God is not your own growing holiness (good and necessary, but never complete this side of glory), but the alien righteousness of Christ credited to your account. Paul's language is commercial: Abraham's faith was counted (Greek logizomai, an accounting term) to him as righteousness (Romans 4:3). The books balance not because Abraham earned it but because God reckoned Christ's righteousness as his. On the cross, God performed a divine exchange: our sins on Christ's record, His righteousness on ours. The Father looks at the believer and sees His Son; He looks at the Son on the cross and sees our sin. This is why the Christian can have present assurance. Your record is Christ's record. That is why the gospel is good news.