Calvin:

Here a question may be raised, how have the sins of the whole world been expiated? I pass by the dotages of the fanatics, who under this pretense extend salvation to all the reprobate, and therefore to Satan himself. Such a monstrous thing deserves no refutation. They who seek to avoid this absurdity, have said that Christ suffered sufficiently for the whole world, but efficiently only for the elect. This solution has commonly prevailed in the schools.  Though then I allow that what has been said is true, yet I deny that it is suitable to this passage; for the design of John was no other than to make this benefit common to the whole Church. Then under the word all or whole, he does not include the reprobate, but designates those who should believe as well as those who were then scattered through various parts of the world. For then is really made evident, as it is meet, the grace of Christ, when it is  declared to be the only true salvation of the world. John Calvin, 1 John 2:2.

[Note: For now I will pass over the question of whether or not Calvin rejects this formula in his Concerning the Eternal Predestination of God, when speaking of this same verse and issue. If we assume, as I think most scholars do, that what Calvin does say here is what he did actually believe, we have to then consider what he meant.

According to AA Hodge, Calvin expressed his commitment to the classic ‘unrevised’ formula. Thus the idea that Calvin thought only that the “suffering for all” referred to a mere hypothetical suffering for all is not credible. On the contrary, from his wider writings it is more than clear that Calvin considered this suffering for all, actual and not hypothetical.

For example:

To be short this is that the Apostle says in the tenth of Hebrews, if we will be partakers of all that was gotten us by the son of God, we must have patience: after that he has shown himself, that when Jesus Christ had suffered for the sins of the world, he went up into heaven, he added “That this was to arm us to patience.” For it is nothing, if the fruit of this redemption, which was purchased for us, does not show itself by faith: for otherwise, it will be a thing come to nought. John Calvin, Sermons on 1 Timothy, Sermon 51, 6:13-16, p., 612.

Since then, this robber was a man disapproved of by all, and God called him so suddenly, when our Lord made effective for him His death and passion which He suffered and endured for all mankind, that ought all the more to confirm us…. But though our Lord Jesus Christ by nature held death in horror and indeed it was a terrible thing to Him to be found before the judgment-seat of God in the name of all poor sinners (for He was there, as it were, having to sustain all our burdens), nevertheless He did not fail to humble himself to such condemnation for our sakes…. John Calvin, Sermons on the Deity of Christ, Sermon 9, Matt 27:45-54, pp., 151, and 155-156.

And then the question moves to, in Calvin’s mind, what did Christ suffer?, in his suffering for all? To answer that, see Calvin.]