Jag funderar på om vi ska gå hem nu.

In this sentence, jag funderar på means something like I’m thinking about, I’m considering, or I’m wondering about.

So:

• Jag funderar på om vi ska gå hem nu = I’m wondering whether we should go home now

A useful point is that fundera på often suggests a process of thinking something over, not just having a quick thought.

Because fundera på is the normal expression in Swedish for think about / consider.

• fundera = think, ponder
• fundera på = think about, consider

So Swedish treats this as a verb + preposition combination.

Examples:

• Jag funderar på saken. = I’m thinking about the matter.
• Hon funderar på att flytta. = She’s thinking about moving.

With om-clauses, you can also get:

• Jag funderar på om... = I’m thinking about whether...

Here, om means whether.

So:

• om vi ska gå hem nu = whether we should go home now

This is a very common use of om in Swedish after verbs like:

• undra = wonder
• fråga = ask
• veta = know
• fundera på = think about / wonder

Examples:

• Jag undrar om han kommer. = I wonder whether he’s coming.
• Hon vet inte om det är sant. = She doesn’t know whether it’s true.

Note that om can also mean if, so the exact English translation depends on context.

Ska is used to express an idea like should, going to, or sometimes are to depending on context.

Here, vi ska gå hem nu means something like:

• we should go home now
• we’re supposed to go home now
• we’re going to go home now

In this sentence, the most natural interpretation is whether we should go home now.

So:

• går hem nu = go/goes home now or are going home now
• ska gå hem nu = should go home now / are going to go home now

Because after ska, Swedish uses the infinitive without att.

So:

• ska gå
• ska äta
• ska komma

This is similar to English should go, will come, where you also do not add to after the modal verb.

Compare:

• Jag vill gå. = I want to go.
  (No att after vill either.)
• Jag försöker att gå. / Jag försöker gå.
  (att may appear with some other verbs.)

But with ska, you simply say:

• vi ska gå

Because after om introducing a subordinate clause, Swedish uses subordinate clause word order.

So the pattern is:

• om + subject + verb
• om vi ska...

Not:

• om ska vi... ✗

This is an important contrast:

• Main clause question: Ska vi gå hem nu? = Should we go home now?
• Embedded/subordinate clause: Jag funderar på om vi ska gå hem nu. = I’m wondering whether we should go home now.

In other words, Swedish does not keep question word order inside this kind of clause.

Because hem often works like an adverb in Swedish and means home in the sense of to home / homeward.

So Swedish usually says:

• gå hem = go home
• komma hem = come home
• åka hem = go home / travel home

This is very similar to English, where we also usually say go home, not go to home.

If you want to refer to the home as a noun in some other sense, then Swedish uses a noun phrase, but in everyday movement expressions, hem by itself is normal.

Both can mean go home, but they suggest different ways of getting there.

• gå hem = walk home or more generally go home
• åka hem = go home by vehicle or travel home

In many contexts, gå hem can be understood more generally as leave and head home, even if you are not literally walking. But if the means of transport matters, Swedish often distinguishes them.

Examples:

• Vi går hem nu. = We’re going home now.
• Vi åker hem nu. = We’re heading home now (probably by car, bus, train, etc.)

Nu means now, and it gives the sentence a sense of immediate timing.

So:

• gå hem nu = go home now

Without nu, the sentence would be more general:

• Jag funderar på om vi ska gå hem. = I’m wondering whether we should go home.

With nu, the speaker is thinking about the present moment: is this the time to leave?

Yes. Jag undrar om vi ska gå hem nu is very natural and common.

The difference is mostly one of nuance:

• Jag undrar om... = I wonder whether...
• Jag funderar på om... = I’m thinking about whether... / I’m considering whether...

Funderar på can sound a little more like you are actively weighing the idea.
Undrar can sound a little more like you are simply wondering.

In many everyday situations, both work well.

A rough breakdown is:

• Jag = I
• funderar på = am thinking about / am considering
• om = whether
• vi = we
• ska = shall / should / are going to
• gå = go
• hem = home
• nu = now

So very literally, it is something like:

• I am thinking about whether we shall go home now

That literal version sounds a bit stiff in modern English, so a more natural translation is:

• I’m wondering whether we should go home now.