Stigafjöldinn er hár.

It is a compound noun:

• stig(a)- = points (from stig)
• fjöldi = number, amount, total
• -inn = the (the suffixed definite article)

So stigafjöldinn literally means the number of points or the point total.

The -a- in the middle is there because stig appears in the genitive plural form stiga inside the compound.

In Icelandic, the definite article is very often attached directly to the noun.

So instead of a separate word like English the, Icelandic commonly says:

• stigafjöldi = point total / number of points
• stigafjöldinn = the point total / the number of points

This suffixed article changes form depending on gender, number, and case. Here -inn is the correct nominative singular definite ending for this masculine noun.

Because the subject is grammatically singular.

Even though stig refers to multiple points, the head noun is fjöldi = number/total, and that noun is singular. So the verb must also be singular:

• Stigafjöldinn er hár. = The point total is high.

If the subject were plural, then you would use eru.

Hár is the masculine singular nominative form of the adjective hár = high.

It matches stigafjöldinn, which is:

• masculine
• singular
• nominative

After the verb er, Icelandic adjectives still agree with the subject in gender, number, and case when they describe it.

So:

• masculine singular nominative: hár
• feminine singular nominative: há
• neuter singular nominative: hátt
• plural nominative: háir / háar / há

Because hátt is the neuter singular form, and stigafjöldinn is not neuter — it is masculine.

A very common learner issue is to think of the adjective more like an adverb or some general default form, but here it is a normal adjective describing the subject, so it must agree with the noun:

• stigafjöldinn → masculine singular
• therefore hár

So Stigafjöldinn er hár is correct, not Stigafjöldinn er hátt.

It is in the nominative singular.

This is because it is the subject of the sentence:

• Stigafjöldinn = subject
• er = verb
• hár = predicate adjective

A simple way to think about it is: the thing that is something usually appears in the nominative in this kind of sentence.

This is a very common pattern in Icelandic compounds. The first noun often appears in a genitive form.

Here:

• stig = points
• genitive plural = stiga
• stiga + fjöldi = number of points

So stigafjöldi literally has the structure number of points.

English often uses of, but Icelandic frequently builds this idea into a compound instead.

Yes, that is possible and understandable.

• Fjöldi stiga er hár. = The number of points is high.
• Stigafjöldinn er hár. = The point total is high / The number of points is high.

The compound version is very natural in Icelandic. The version with separate words can also work, but the exact choice depends on style, definiteness, and context.

The sentence you were given uses the definite compound noun, which is compact and very idiomatic.

Yes. Icelandic very often forms long compound nouns instead of using separate words the way English does.

So something like number of points easily becomes one word:

• stiga + fjöldi → stigafjöldi

This is one of the most important habits to get used to in Icelandic. When you see a long word, try to identify:

1. the last part, which is usually the main noun
2. the earlier part(s), which describe it

Here the main noun is fjöldi.

A rough guide is:

• Stigafjöldinn ≈ STI-ga-fyul-din
• er ≈ ehr
• hár ≈ howr (but with Icelandic á, a long ow/au-like vowel)

A few helpful notes:

• Stress in Icelandic usually falls on the first syllable: STIgafjöldinn
• ö does not sound like English o; it is closer to a front rounded vowel
• ð in Icelandic is like the th in this, though in some positions it can be weaker

Exact pronunciation varies a bit, but first-syllable stress is very important.

It comes after the verb because it is a predicate adjective.

Structure:

• Stigafjöldinn = subject
• er = is
• hár = adjective describing the subject

So the pattern is:

• The point total is high
• Stigafjöldinn er hár

This is different from an attributive adjective, where the adjective comes directly before the noun. Here it is not a high point total, but rather the point total is high.

Yes. Depending on context, stig can mean things like:

• point(s) in scoring
• step(s)
• degree(s)

So a compound with stiga- can sometimes be ambiguous in isolation. In actual context, though, the meaning is usually clear.

In this sentence, the meaning shown to the learner determines which sense is intended. Grammatically, the structure works the same way either way: stiga- is the dependent part of the compound, and fjöldi is the main noun.