According to H.W. Fowler's delightfully stern guide to English grammar, "The King's English", the correct usage of will and shall has several contributing factors.

Firstly, in Old English the terms were used without an association with the future. "Shall" was concerned with an obligation, and "will" with a wish. Because commands and wishes are fulfilled in the future, tense auxiliary forms grew out of this usage.

In the "coloured future" the terms retain their association with obligation and desire. So "I shall write this report" implies that I am required to write it, and "I will write this report" implies that I want to write it.

The correct usage stems from the idea that "I shall..." is redundant because one doesn't command oneself to do something. "Shall I..." is fine. "I will... ", "We will...", "Will she...?" and "Will they...?" are fine, however "You will..." doesn't work, because we don't know the other's mind.

Those who wish for a fuller understanding of this area and how it impacts other tenses and usages could try struggling though Fowler's 1908 edition of the work, at

But as the man himself notes about the difference between will and shall...:

"It is unfortunate that the idiomatic use, while it comes by nature to southern Englishmen (who will find most of this section superfluous), is so complicated that those who are not to the manner born can hardly acquire it; and for them the section is in danger of being useless. In apology for the length of these remarks it must be said that the short and simple directions often given are worse than useless. The observant reader soon loses faith in them from their constant failure to take him right; and the unobservant is the victim of false security. "

I have been taught, but now do not believe, that it is correct to use 'shall' in the first person and 'will' in the second and third persons for the simple form of the future tense, and vice versa for the emphatic form. This is an ideal example of picky grammarian rules. I now endorse the Swedish usage, whereby 'shall' (skall) indicates an essentially inevitable event, 'will' (vill) indicates an intention, and neither is the standard means of expressing the future.

(BTW, the sense of the English will is better expressed in Swedish by 'borde' - 'vill' being used strictly to indicate intention or desire. Thanks to bigmouth_strikes for the advice.)
Traditionally, the correct way to use will and shall is as Tiefling gives it. To state it fully:

To express future time: shall goes with the first person, will with the second and third persons.

To express an intention to act: will goes with the first person, , shall goes with the second and third.
It is uncertain whether or not this distinction was ever part of normal everyday usage, or if this is wishful thinking on the part of the grammarians.

In modern usage, shall has almost completely been dropped from use when talking about the second or third persons, and is used apparently at random when talking in the first person. I have never met nor heard of anyone who insisted on the traditional usage of these words.

In Germanic languages other than English, will and shall are used differently that in English. German parallels Old English usage, in that `wollen' (will) indicates a desire: Ich will nach Hause fahren: I want to drive home. `Sollen' (shall) marks an obligation: Ich soll Kants Kritik lesen: I should/shall read Kant's Critique. Neither makes explicit reference to the future, but there is often an implicit connection: if I want to, or am obligated to, do something, I probably haven't done it yet. In German, the pure future is expressed with `werden' (to become): Sie wird ihre B├╝cher verkaufen: She will sell her books.

Dutch has a similar distinction between `willen' (will) and `zullen' (shall). However, the pure future is also expressed with `zullen': Zij zullen een dag sterven: One day they will die.

Apologies for my (probably bad) sentences. I can hardly be said to speak any language but English. And remember, kids: Germanic languages have no future tense.

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