Tämä on pieni ihme.

• Tämä = this
• on = is (from the verb olla, to be)
• pieni = small, little
• ihme = miracle, wonder

So the sentence is literally This is a small miracle.

On is the 3rd person singular form of olla (to be).

Here, the subject is tämä (this), which takes the same verb form as he/she/it in English:

• minä olen = I am
• sinä olet = you are
• hän on = he/she is
• tämä on = this is

So Tämä on... means This is...

Because this sentence is in the basic nominative form.

In Tämä on pieni ihme, the phrase pieni ihme is a predicate noun phrase after on (is), and in a simple affirmative sentence like this, both words normally stay in the nominative singular:

• pieni = small
• ihme = miracle

So:

• Tämä on pieni ihme = This is a small miracle

Forms like pienen ihmeen belong to other grammatical contexts, not this basic one.

Finnish has no articles, so there is no separate word for a, an, or the.

That means ihme can mean:

• a miracle
• the miracle
• sometimes just miracle, depending on context

The exact meaning comes from the situation, not from an article.

So pieni ihme naturally translates as a small miracle here.

Usually, yes. In ordinary Finnish, adjectives typically come before the noun:

• pieni ihme = small miracle
• suuri talo = big house
• kaunis päivä = beautiful day

Also, the adjective usually matches the noun in number and case, though here both are in the basic singular form.

A simple pronunciation guide:

• Tämä ≈ TAE-mae
• on ≈ on
• pieni ≈ PIE-eh-nee
• ihme ≈ EEH-meh

A few useful notes:

• ä is not the same as English a. It is more like the vowel in British cat for many speakers.
• Finnish words are usually stressed on the first syllable:
  • TÄ-mä
  • PIE-ni
  • IH-me

Yes, you could say Se on pieni ihme too, but the nuance is a little different.

• tämä = this
• se = usually that, though in spoken Finnish it is also very commonly used where English would say it or even this/that depending on context

So:

• Tämä on pieni ihme = This is a small miracle
• Se on pieni ihme = That/It is a small miracle

If you are pointing to something close or introducing something directly, tämä is very natural.

Yes. Ihme can mean:

• miracle
• wonder
• something surprising or amazing

So pieni ihme can sound slightly idiomatic in some contexts, like English a small miracle meaning something unexpectedly fortunate or impressive.

For example, if something worked despite difficulties, a Finn might call it pieni ihme.

The normal neutral order is:

Tämä on pieni ihme.

Finnish word order is somewhat flexible, but changing it usually changes the emphasis.

For example:

• Tämä on pieni ihme. = neutral statement
• Pieni ihme tämä on. = more marked, something like This really is a small miracle

For beginners, the standard subject + verb + complement order is the safest choice.

Because the sentence talks about one thing:

• Tämä = this
• Nämä = these

If it were plural, you might get:

• Nämä ovat pieniä ihmeitä. = These are small miracles.

In your sentence, everything is singular:

• tämä = this
• on = is
• pieni ihme = a small miracle

Yes. It sounds perfectly natural in Finnish.

It could be used when something surprising, lucky, or impressive happens, for example:

• a machine starts working again
• a child finally falls asleep
• a difficult task succeeds

So Tämä on pieni ihme can be both literal and slightly expressive, just like This is a small miracle in English.