Objectives: To develop a simple, practical methodology to equate or link equivalent domains of the 36-item Short-Form Health Survey (SF-36) and the Patient-Reported Outcomes Measurement Information System 29-item questionnaire (PROMIS-29) using the Rasch framework. Study design and setting: In April 2016, the PROMIS-29 and SF-36 were completed by 1501 individuals selected to be representative of the French population. For each domain common to the two questionnaires, a Partial Credit Model was fitted to the items related to that dimension in the two questionnaires. These items were then calibrated on the same metric, which enabled the scores from one questionnaire to be associated with the scores from the other. Results: Six of the seven PROMIS-29 scales and five of the six SF-36 subscales (physical, pain, social, vitality, depression and anxiety domains) were equated or linked. Correspondence tables between scores, with a 95% confidence interval, were established for each domain. A freely available Stata macro program was developed to automatize the equating or linking process. Conclusion: These results should facilitate comparisons across studies using the SF-36 and the PROMIS-29 in France. The equating or linking process developed is simple to implement and can be used in other countries and for other instruments.