Will is the usual way to talk about the future, while shall today lives mainly in offers and suggestions with I and we: Shall I open the window?, Shall we go? Will doesn't work here: Will I open the window? asks about the future rather than offering help. Elsewhere, shall sounds formal or old-fashioned.
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will + verb (future); Shall I + verb? (offer to help); Shall we + verb? (suggestion)
- The new bus timetable will start next Monday, so check your route.
- Shall I book a table for six, or is that too many?
- It's getting late. Shall we take a taxi home?
What changed
First versionWill I make you a coffee while you finish the report?
RevisionShall I make you a coffee while you finish the report?
An offer is about something you're going to do, so the future with will seems logical, hence Will I. But that asks what is going to happen, not whether the other person wants your help. An offer needs Shall I, which replaced Will I.
In American English, Shall I…? sounds rather formal, and people more often say Should I…? or Do you want me to…?: Should I call a taxi? In contracts, shall expresses an obligation: The tenant shall pay the rent by the fifth of each month.
Your turn
You look cold. ___ I close the window?
Show the answer
Shall — The speaker is offering help, and an offer with I uses Shall: Shall I close the window? Will I close the window? would ask whether I'm going to close the window at some point in the future, and it sounds strange here.
Before a meeting, make a colleague two offers in one sentence: to help with one task (Shall I…?) and to do something together (shall we…?).
Shall I print the agenda for everyone, and shall we grab a coffee before we start?
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