Pure modal auxiliary verbs one by one

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There is a general guide to modality and modal auxiliary verbs which you should follow before you access this area. This section focuses only on true, central or pure modal auxiliary verbs. There is another guide to semi-modal auxiliary verbs which covers dare, need and used to and marginal modal auxiliary verbs such as seem to, tend to, be about to etc.
An alternative view is presented in the guide to types of modality.

What follows is a guide to the main modal auxiliary verbs in English, taken one by one. We will look at the possible functions of each modal and how it is used.
Sections in this colour in the notes following each table concern areas which cause specific and predictable problems for learners. It is these in particular that you must be able to analyse and explain in the classroom.
Tests in sections of this page only exist for the more complex verbs but there's a link to a test on all of them at the end. Try it now if you like.

The identification of pure modal auxiliary verbs is often limited to 9 verbs:
can, could, may, might, must, shall, should, will and would.
In this analysis, however, two more are included, the verbs had better and ought to, which share structural characteristics with the central nine.
Elsewhere, you will find verbs included in or excluded from this list. If you have followed the essential guide to this area you may recall the following section.
Traditionally, in order to be included as a pure or central modal auxiliary the verb needs to conform to some tests:

The verbs cannot co-occur (appear together) so, for example:
    *I must can do it
    *I will must do it
are impossible because both must and can are pure or central modal auxiliary verbs. However
    I may be able to do it
    I will have to see him
are possible so be able to and have to are not, by this test pure modal auxiliary verbs.
The verbs do not change to show person so in, for example:
    He has to go but that aren't able to
the verb have changes to has and the verb be changes to are but:
    *She musts come
    *He wills do it
are not possible so must and will are both pure modal auxiliary verbs but have to and be able to are not.
The verbs are used to form negative and questions by being moved to the beginning of the clause or being followed directly by not so:
    I will not do it
    May she come?
    I can't go
are all possible as are
    She didn't have to go
    They didn't need to go
but
    *Do I must see him?
    *They don't should be here
etc. are not possible so must and should are pure modal auxiliary verbs and the others are not in the same class.

You can use this menu to go to the verb which interests you or work through the page, taking the tests as you go along.

could might should would must can may will shall ought to had better

could / was able to

Essentially, could performs the following functions in English:

Function	Example
present possibility	That could be the postman now.
future possibility	It could rain tomorrow.
past possibility	He could have seen her. I'm not sure.
present ability	I could help with that, if you like.
future ability	I could finish in an hour if I get some peace.
past ability	When I was only two, I could swim pretty well.
permission	Could I ask you a question?
complaint	You could have warned me!

Notes:

Present possibility and future possibility are not always easy to distinguish. For teaching purposes, it's rarely important to do so because the forms and functions are the same.
Most uses of could refer to possibility or ability.
    She could have left her keys with John
can refer to both possibility and ability. It means either:
    John offered to look after the keys so she was able to leave them with him
or
    It is possible that she left her keys with John (and that's why she can't find them now)
Only the second use of could can be replaced with might (see below).
be able to is only an alternative if the sense expresses ability. General ability in the past can be expressed either with could or was able to:
    I could speak French = I was able to speak French.
However, if we refer to a specific instance of success, only was able to is possible:
    I was able to say the word in French
NOT
    *I could say the word in French.
When used for permission, the verb is generally confined to formal(ish) questions.
For the negative deduction uses of could/couldn't have, see under must below.
When used for complaints, the verb is usually interchangeable with might and always in the perfect tense.
When used for future ability or possibility, the question forms often imply a request rather than an enquiry about ability or possibility. For example:
Could you open the door?
is not about enquiring about future ability but it could be enquiring about past ability or a request for some help.

Try the test.

might

Essentially, might performs the following functions in English:

Function	Example
present possibility	Careful. There might be a snake in the hall.
future possibility	It might rain tomorrow.
past possibility	He might have telephoned while I was out.
suggestion	You might try taking an aspirin.
permission	Might I talk to you?
complaint	You might have warned me!

Notes:

Some of these are quite unusual and wouldn't be taught at lower levels. E.g., might for permission and suggestions.
might never refers to ability so:
She might have left her keys with John
can only refer to possibility: it means
It is possible that she left her keys with John (and that's why she can't find them now)
This use of might can also be replaced with could (see above).
The negative of the use for permission is usually expressed with mustn't or can't:
We mustn't/can't go
The negative of the use for past possibility:
when the speaker is quite sure of something this is usually expressed using couldn't have/can't have:
He couldn't / can't have got out
when the speaker is unsure we use might:
He might not have tried to telephone me
might is often seen as adding 'distance' – making possibilities less likely and requests or suggestions more polite. Compare
It could/might rain
Could/Might I go now?
etc.

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should

Essentially, should performs the following functions in English:

Function	Example
advice	You should see a doctor.
obligation	You should not talk that way!
conditional uses	We should love to come (if we are invited).
logical deduction	Mary should be home soon.

Notes:

The distinction between strong advice and obligation is often blurred – the roles of the speakers usually give the game away. If someone in authority uses should it usually expresses obligation.
The conditional use of should for 1st person forms instead of would is often seen as formal and pretty much confined to British English. This is also called the contingent use.
should is occasionally used in rather odd, formal expressions such as:
I regret that it should have happened.

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would

Essentially, would performs the following functions in English:

Function	Example
request/volition	Would you leave me alone, please?
conditional uses	You would be in danger if you tried it without training.
habit	We would always have tea at 5.
characteristic	That's just the sort of thing he would say.

Notes:

Would is one of the most common words in English, ranking approximately in 60th place.
The conditional uses are extremely common. This is also called the contingent use.
When used to describe past habit, it follows an initial use of used to and often expresses nostalgia.
When followed by rather, with or without ... than ..., the modal indicates preference:
I'd rather stay in and watch television (than ...).
There is a slightly unusual use of would to express an uncertain deduction (see under will below). Compare, e.g.,
That'll be Mr. Brown you saw in the classroom
and
That would be Mr. Brown you saw in the classroom.

Try the test.

must / have to / needn't

Essentially, must performs the following functions in English:

Function	Example
obligation	Must I take the test?
logical deduction	That must be his brother. Aren't they alike?
advice	You really mustn't make such a fuss.

Notes:

The difference between strong advice and obligation is often very blurred (if it exists at all).
must can be replaced by have to in certain circumstances only.
External vs. internal obligation: it is often asserted that have to implies an external obligation but must refers to an internal one. Compare
    I must get this done
which can mean that this is a self-imposed obligation, with
    I have to get this done
which can imply an external obligation.
Too much can be made of this dubious distinction and it's probably not worth teaching it because native speakers use the verbs in free variation in most cases.
Tenses: must has no future or past forms for obligation (but it does in the sense of deduction, see note 4.) so the use of have to is obligatory in, e.g.:
    I had to do it
    We'll have to wait and see
etc.
The negative of must for obligation has two forms:
1. No obligation: needn't/don't have to
    You needn't/don't have to go)
Only didn't have to/didn't need to express a lack of obligation in the past. The expression needn't have suggests something was unnecessarily done. Compare
    He didn't need to do it (so didn't)
with
    He needn't have done it (but did).
2. Negative obligation: must not
    You mustn't go
The negative of the use for deduction in standard British English is formed with could not or cannot:
    He can't have done it by himself
    It couldn't have been the same man
However, in some varieties must not is used for a negative logical deduction.
This sense of the verb does have a past form:
    He must have escaped
    He couldn't have known
etc.

can / able to

Essentially, can performs the following functions in English:

Function	Example
ability	Can you do it before tomorrow?
permission	You can go now.
possibility	The weather can be dreadful in March.
request	Can you help me?

Notes:

When the request form uses the 1st person, it functions as an offer:
Can I help?
The negative of the permission function can be expressed using can or must:
You can't leave yet
You mustn't leave yet
cannot have/can't have only occurs as negative past deduction (see under must). It is not used for permission or ability in the past.
be able to is only an alternative if the sense expresses ability:
    I can speak French = I am able to speak French
However, able to is NOT possible in other senses: you can't give permission by saying:
    *You are able to ask questions at the end
and there is a functional difference between:
    Are you able to help me?
and
    Can you help me?
The first enquires about ability and the second about willingness so it's a request).
Like must, can has no future form (although it does have a past in some senses of ability only (see under could, above)). For this reason, future senses are expressed as follows:
Future ability:
    She will be able to help tomorrow
    She can help tomorrow
In the second of these examples, there is a possible ambiguity because it also has the meaning of
    I will allow her to help tomorrow
Future permission:
    They will be allowed to go later
    They can go later
Future possibility:
    The weather might be dreadful next March
but
    *The weather can be dreadful next March
is not possible).

may

Essentially, may performs the following functions in English:

Function	Example
permission	May I sit here?
possibility/doubt	That may be his brother.

Notes:

The permission use is often seen as a more formal version of can. Compare might.
The possibility use often implies less likelihood than could. Compare
I can be cold in April
with
It may be cold in April
The former also implies in general whereas the latter often refers to a particular future.
The negative is slightly peculiar:
may not cannot express impossibility. We use can't/couldn't:
That can't/couldn't be his brother
for that function. It can, however, express doubt in, e.g.:
That may not be what you need
may not for prohibition (i.e., negative permission) is used but is rarely contracted to mayn't.

will

Essentially, will performs the following functions in English (see also the section on tenses for the use of will to talk about the future):

Function	Example
requests	Will you walk this way?
logical deduction	That will be the postman.
intention	I'll write when I can.
insistence	He will keep complaining.
ability	The restaurant will seat 50 people

Notes:

The insistence use never contracts will to 'll.
The intention use is almost always only first person unless we are reporting what someone else intended to do:
    I'll come early to help
    He said he'll write when he can
    You said you'll do it
etc.
The negative of the use for deduction is often formed with cannot:
That can't be the postman
but if the speaker is more certain or is basing the statement on evidence or experience then won't can be used:
That won't be the postman; it's too early.
The use for ability is somewhat formal and may be replaced by the present simple tense.

shall

Essentially, shall performs limited modal functions in English (see also the section on tenses for the use of shall to talk about the future):

Function	Example
suggestion/offer	Shall we go? Shall I help?
obligation	That shall not happen.

Notes:

The suggestion/offer use only occurs as an interrogative. This use is confined to the first person, singular or plural.
The obligation function expresses great determination and is generally perceived as formal.
In neither function can the verb be contracted to 'll.

ought to

Essentially, ought to performs the following functions in English:

Function	Example
obligation	You ought to go.
logical deduction	She ought to be here around 6.
advice	You ought to take him to the vet.

Notes:

The difference between strong advice and obligation is often very blurred (if it exists at all).
It is often asserted that ought to implies a sense of duty rather than pure obligation or advice. Compare:
You should write to him
with
You ought to write to him
For most learners of English, this is irrelevant.
(This distinction may stem from the fact that ought is an old past participle form of the verb owe and we owe a duty.)
The negative of ought to for obligation has two forms:
1. No obligation: needn't/don't have to:
You needn't / don't have to go
2. Negative obligation: ought not:
You oughtn't (to) go.
Omitting the 'to' is rare and formal.
The negative of the use for deduction is formed with cannot:
She can't have left already
There is some evidence of the existence of ought as a non modal with forms such as:
You didn't ought to do that
Did he ought to ask permission?
etc.
Such forms are at best non-standard; many would consider them illiterate.
In American English in particular (but increasingly evident in other standards) the bare infinitive is quite common in the negative:
You oughtn't do that

had better

This structure is not considered a pure modal in all analyses but it is included here because it acts like a modal in most ways.
Essentially, had better performs the following functions in English:

Function	Example
advice	You had better wear something warm on the boat trip.
warning / threat	You had better not do that again or there'll be trouble.
future (desperate) wishes	It had better rain soon or the garden will die.
suggestions	Hadn't we better ask for permission?

Notes:

The had is frequently contracted to 'd, causing some to confuse it with would.
The form is only used for present or future events. There is no past form and in reported speech the verb is often replaced:
He said we shouldn't do it
or remains unchanged
She told us we had better not be late
The negative form for advice is formed as had better not.
There is a common negative question form for tentative suggestions:
Hadn't you better get some sleep?
The advice function only refers to specific situations or actions. Compare:
    You had better not listen to him
with
    *You had better not listen to bad advice
For general situations or actions rather than specific ones, the preferred verb is should:
    You should not listen to bad advice.
The warning / threat function is often implicit in the verb:
You had better not be late
may be responded to with
Or else?
The verb should does not routinely imply this.
The functions of hopes and warnings usually refer to a near future. Hence the form is often accompanied by time adverbials such as soon:
You had better finish that soon
He had better arrive in the next day or so or he'll be too late
The form is often used as an ersatz conditional:
You had better do that carefully or you'll get paint on the floor
equals
If you don't do that carefully, you'll get paint on the floor
Informally, better may be replaced with best:
You'd best tell the truth
Some consider this colloquial or even illiterate.
Question forms are formed as for other modal auxiliary verbs but are quite formal and rarer:
Had I better talk to him?
In fact, the negative question form is a lot more common:
Hadn't I better talk to him?
The form is not used to talk about preferences (that's the function of would rather, see above under would).
The form cannot be used for obligation.
In rapid speech the 'd is often not audible and the form sounds like, e.g., you better, leading some to leave the word out deliberately in speech and in writing.

Summary

Here's a summary diagram of much of this.

summary

Try a test on all these modal auxiliary verbs.

Related guides
essential guide to modality	for a simpler guide in the initial training section
modal auxiliary verbs: tense and aspect	for a more technical guide in the in-service section which considers the modal auxiliary verbs in relation to perfect and progressive forms
semi-modal auxiliary verbs	in the in-service section and which also considers marginal modal auxiliary verbs such as seem, tend, be about to etc.
complex tenses	in the in-service section which also considers complex tenses in relation to modality (I shouldn't have done it etc.)
teaching modality	for some ideas on how to use the analysis above
types of modality	for a more technical guide to types of modality such as epistemic and deontic modality