The Tens and the Vigesimal System (50-90) | Danish Grammar

This is the page where Danish numbers stop looking like English ones. The tens up to 40 are familiar enough, but from 50 to 90 Danish counts in twenties — a vigesimal (base-20) system inherited from Old Norse. Halvtreds (50), tres (60), halvfjerds (70), firs (80), halvfems (90) cannot be derived from the units the way fifty comes from five. They are built on multiples of twenty, with a halv- prefix that does something genuinely clever once you decode it. Most resources tell you to "just memorise" these. We are going to actually explain them — and once the halv- logic clicks, they stop being arbitrary.

First, the easy tens: 20, 30, 40

Three of the tens are essentially decimal and give no trouble:

Number	Danish	Notes
20	tyve	the base unit "twenty"
30	tredive	"three-ten," decimal-style
40	fyrre	shortened from older fyrretyve

Min far fylder fyrre til sommer.

My dad turns forty this summer.

Der var omkring tredive mennesker til mødet.

There were about thirty people at the meeting.

After 40, the system switches gears entirely.

The vigesimal tens: 50, 60, 70, 80, 90

Here is the whole set, with the arithmetic that produces each one. The base unit is tyve = 20, abbreviated below as "×20."

Number	Everyday form	Arithmetic	Full historical form
50	halvtreds	2½ × 20	halvtredsindstyve
60	tres	3 × 20	tresindstyve
70	halvfjerds	3½ × 20	halvfjerdsindstyve
80	firs	4 × 20	firsindstyve
90	halvfems	4½ × 20	halvfemsindstyve

In everyday Danish you use the short forms — halvtreds, tres, halvfjerds, firs, halvfems — exclusively. The long -sindstyve forms are essentially historical/archaic; you should recognise them (they appear on old documents and explain where the short forms come from) but you will never need to say them.

Min mormor er lige fyldt halvfjerds.

My grandma has just turned seventy.

Bilen kostede firs tusind kroner.

The car cost eighty thousand kroner.

Han er i halvfemserne og spiller stadig tennis.

He's in his nineties and still plays tennis.

Decoding tres and firs: the whole multiples

Start with the two without the halv- prefix, because they are the clean ones:

tres = tresindstyve = tre sinde tyve = "three times twenty" = 3 × 20 = 60.
firs = firsindstyve = fire sinde tyve = "four times twenty" = 4 × 20 = 80.

The middle piece, sinde (or -sinds-), is an old word meaning "times" (as in en gang = once, but the older multiplicative "times"). So tresindstyve literally reads "three-times-twenty." Strip it down to the stressed front and you get tres. Same for firsindstyve → firs.

Tres minutter går på en time.

Sixty minutes go into an hour.

Hun løb de sidste firs meter alene.

She ran the last eighty metres alone.

Decoding the halv- prefix: the clever half

Now the three with halv- (50, 70, 90). Here is the single idea that unlocks them. In this old counting system, halv- in front of an ordinal means "half before" that ordinal — i.e. halfway up to it. So:

halvtredje = "half-third" = 2½ (halfway between 2 and 3, i.e. half a unit short of the third)
halvfjerde = "half-fourth" = 3½
halvfemte = "half-fifth" = 4½

This is the same logic preserved in German halb drei = "half three" = 2:30, and in older Danish time-telling halv tre = half past two. Half names the unit you are halfway toward, not the one you've passed.

Now multiply each by twenty:

Word	Reads as	Value	× 20 =
halvtreds(indstyve)	halvtredje sinde tyve	2½ × 20	50
halvfjerds(indstyve)	halvfjerde sinde tyve	3½ × 20	70
halvfems(indstyve)	halvfemte sinde tyve	4½ × 20	90

So halvtredsindstyve literally says "half-third times twenty" = 2½ × 20 = 50. You can see the ordinal hiding inside each short form: halvtreds holds tredje (third), halvfjerds holds fjerde (fourth), halvfems holds femte (fifth).

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The whole trick: halv- means "halfway to the next," so halvtredje = 2½, halvfjerde = 3½, halvfemte = 4½. Multiply by twenty and you have 50, 70, 90. This isn't memorisation — it's one rule applied three times.

Halvtreds plus halvtreds er hundrede.

Fifty plus fifty is a hundred.

Der er halvfems dage til sommerferien.

There are ninety days until the summer holiday.

Why there is no femti

A frequent and very natural mistake — especially for anyone who knows Norwegian or Swedish — is to try to build 50 from the unit fem (five), as femti or femten-style. Danish has no such word. Femten already means fifteen, and there is no decimal femti for fifty at all. You cannot derive the Danish tens from the units; you must go through the base-twenty forms.

This is precisely where Danish diverges from its neighbours. Norwegian and Swedish reformed their tens to be decimal:

Number	Danish	Norwegian	Swedish
50	halvtreds	femti	femtio
60	tres	seksti	sextio
70	halvfjerds	sytti	sjuttio
80	firs	åtti	åttio
90	halvfems	nitti	nittio

Norwegian femti and Swedish femtio are transparently "five-ten." Danish kept the old vigesimal system, which is why Danish numbers are famously the hardest of the three Scandinavian languages for learners — and why a Norwegian femti will simply not be understood as 50 in Danish.

Det hedder ikke femti på dansk — det hedder halvtreds.

It isn't called 'femti' in Danish — it's halvtreds.

Compounds and a bonus: money slang

These tens combine with units exactly like the others, units first, joined by og ("and"): enoghalvtreds (51), femoghalvfjerds (75), otteogfirs (88).

Hun blev otteoghalvfjerds år gammel.

She lived to be seventy-eight.

As a bonus, the vigesimal tens survive in money slang for banknotes (informal). A halvtredser is a 50-krone note, a hundredkroneseddel shortened to a hundredelap, and so on; en tresser, en firser work the same way, and firserne / halvfemserne also name the decades (the 80s, the 90s).

Kan du veksle en halvtredser?

Can you change a fifty (50-krone note)? (informal)

Musikken fra firserne er populær igen.

Music from the eighties is popular again.

Common mistakes

Inventing femti for 50. There is no decimal fifty in Danish; that's Norwegian/Swedish.

❌ Jeg er femti år gammel.

Incorrect — Danish has no 'femti'; fifty is halvtreds.

✅ Jeg er halvtreds år gammel.

I'm fifty years old.

Confusing halvfjerds (70) with firs (80) or halvfems (90). The halv- ones step by twenties: 50, 70, 90; the whole ones are 60, 80. Anchor on the ordinal inside: tred=50, fjerd=70, fem=90.

❌ Min bedstefar er firs — han er født i 1956. (i.e. should be 70)

Mismatch — firs is 80, not 70; seventy is halvfjerds.

✅ Min bedstefar er halvfjerds — han er født i 1956.

My grandfather is seventy — he was born in 1956.

Using the long -sindstyve form in speech. It's archaic; use the short form.

❌ Hun er tresindstyve år.

Archaic/stilted — modern Danish uses the short form tres.

✅ Hun er tres år.

She's sixty years old.

Reading halv- as if it lowered the number ('half of'). Halvtreds is not "half of treds"; halv- means halfway up to the next ordinal, so it gives 2½×20, not 30.

❌ halvtreds = 30 (half of 60)

Incorrect — halv- means 'halfway to the third twenty', so halvtreds = 2½×20 = 50.

✅ halvtreds = 2½ × 20 = 50

fifty

Key takeaways

The tens 20/30/40 (tyve, tredive, fyrre) are decimal-ish; 50–90 are base twenty.
Whole multiples: tres = 3×20 = 60, firs = 4×20 = 80, where -sinde-/-sinds- = "times."
halv- = "halfway to the next ordinal": halvtredje 2½, halvfjerde 3½, halvfemte 4½ → ×20 → halvtreds 50, halvfjerds 70, halvfems 90.
Use the short forms in speech; the long -sindstyve forms are archaic.
There is no femti in Danish — that's Norwegian/Swedish, which went decimal.
The tens live on in money slang (en halvtredser = 50-krone note) and decade names (firserne = the 80s).

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