Vowels
The symbols inside the brackets [ ]
represent the sounds with use of the
International Phonological Alphabet (IPA).
You can read more about the IPA
A a [ɑ]
ta (take)
ha (have)

E e [e]
se (see)
tre (three)

I i [i]
vi (we)
bil (car)

O o [u]
sko (shoe)
sol (sun)

U u [ʉ]
du (you)
tur (tour)

Y y [y]
ny (new)
lyd (sound)

Æ æ [æ]
hær (army)
bær (berry)

Ø ø [ø]
dør (door)
bløt (soft)

Å å [o]
grå (gray)
båt (boat)

II
Long and short vowels
In Norwegian, the distinction between a long and a short vowel can be crucial for separating one meaning from another, as the difference between two words sometimes relies solely on vowel length. In the written language (with a few exceptions), the vowel is short when followed by two or more consonants.
Long vowel: tak [tɑ:k] (roof)
Short vowel: takk [tɑk] (thanks)
Long vowel: gul [gʉ:l] (yellow)
Short vowel: gull [gʉl] (gold)
Long vowel: vin [vi:n] (wine)
Short vowel: vinn [vin] (win)
Long vowel: kor [ku:r] (choir)
Short vowel: kopp [kop] (cup)
Did you notice the vowel change in the last pair (marked in red)? Yes, there are some
exceptional rules!
Vowels - exceptional rules
Here I will warn that I'm using the brackets / / instead of [ ]. The / / brackets contain a Norwegian letter - not an IPA symbol.
In word stems, /e/ is pro-nounced like /æ/ before /r/.
e.g. her [hæ:r] (here)
When /o/ is short, it is pronounced like /å/.
e.g. stopp [stop] (stop)
/u/ is pronounced like /o/ when followed by /ng/
e.g. ung [uŋ] (young)
III
Diphthongs
In written Norwegian, there are four diphthongs (barring some rare cases).
ai [ɑi]
mai (May)
kai (quay)
au [ɑu] [øu]
saus (sauce)
pause (pause)
ei [æi] [ei]
hei (hi)
leie (rent)
øy [øy]
høy (high)
øye (eye)
As is common with many aspects of the the Norwegian language, there are dialectal variations in the pronunciation of diphthongs. Notably, /au/ and /ei/ are pronunciated [æu] and [æi] in the areas around Oslo, whereas in many other regions of Norway, they are articulated as [øu] and [ei].
IV
Here you can listen to the same piece of text read in different dialects.
And what they are saying is:
"Vi spiser pizza hver helg. Jeg elsker pizza, men jeg liker ikke løk, så den pleier jeg å plukke av."
(We eat pizza every weekend. I love pizza, but I don't like onion, so I usually pick it off.)
And here is another collection of dialects from NTNU.