У грудні я вдома.

Because after у / в meaning in with a month name, Ukrainian normally uses the locative case.

So:

• dictionary form: грудень = December
• after у / в: у грудні = in December

This is the regular pattern for months:

• у січні = in January
• у лютому = in February
• у березні = in March
• у грудні = in December

So грудні is not a different word; it is the locative form of грудень.

Here у means in.

Both у and в can mean in in Ukrainian. Very often the choice depends on sound and ease of pronunciation, not meaning. Ukrainian likes to avoid awkward sound combinations.

So:

• У грудні я вдома.
• В грудні я вдома.

Both can be understood, but у грудні sounds smoother and more natural to many speakers here.

A useful rule: Ukrainian often switches between у and в for euphony, while the meaning stays the same.

In the present tense, Ukrainian usually does not use a verb equivalent to English am / is / are in sentences like this.

So English:

• I am at home

becomes simply:

• Я вдома

There is no need to add є here. In modern Ukrainian, leaving out the present-tense to be is normal.

So У грудні я вдома is a complete sentence even though it has no separate word for am.

Вдома is an adverb, and it means at home.

It does not literally work like a noun phrase such as in the house. It functions more like a fixed adverbial expression.

Compare:

• Я вдома. = I am at home.
• Я в домі. = I am in the house/building.

So вдома usually refers to being at one’s home in a general sense, not specifically inside a physical building as an object.

They are very close, but вдома is generally the safer standard form for learners.

• вдома = standard/common Ukrainian for at home
• дома = also used by many speakers, but can sound more colloquial, regional, or influenced by everyday speech habits

If you are learning standard Ukrainian, it is best to use вдома.

Yes. Ukrainian word order is fairly flexible, and changing it often changes emphasis, not the basic meaning.

For example:

• У грудні я вдома. → emphasis on in December
• Я вдома у грудні. → more neutral or emphasis on I am at home
• Я у грудні вдома. → also possible, depending on context

The sentence you have, У грудні я вдома, naturally highlights the time: In December, I’m at home.

You can leave it out in the right context, because Ukrainian verb forms often show the subject. But here there is no present-tense verb form to identify the subject, so leaving out я can make the sentence less clear unless the context already tells us who is meant.

So:

• У грудні я вдома. = clear on its own
• У грудні вдома. = possible in context, but incomplete by itself for many situations

For a learner, keeping я is a good idea unless the context makes the subject obvious.

Because у / в with a time expression meaning in takes the locative case, not the accusative.

So:

• грудень = nominative dictionary form
• у грудні = locative, used after у / в for in December

Using у грудень would not be correct for the meaning in December.

A simple learner-friendly guide:

• грудні ≈ hrood-NEE
• вдома ≈ vdo-MA

A few useful notes:

• Ukrainian г is usually pronounced like an English h sound, not a hard g. So грудні starts more like hr- than gr-.
• The stress is:
  • груднí
  • вдомá

If you want to sound natural, stress matters a lot in Ukrainian.

Yes. This is the normal pattern.

To say in a month, Ukrainian usually uses:

• у / в
  • month name in the locative case

Examples:

• у січні = in January
• у квітні = in April
• у листопаді = in November
• у грудні = in December

So У грудні я вдома follows a very common and useful structure.