People say that the Danish number system is impossible, confusing, or just plain weird.

I’m not going to lie to you – it is a little bit weird.

While most languages (like English, German, and Spanish) count based on a system of 10, Danish holds onto an old traditional way of counting based on a system of 20. This is called a vigesimal system.

It’s actually very similar to how the French say 80 (quatre-vingts or “four-twenties”). The difference is that the Danes take it a step further.

But don’t panic. As a teacher of Danish, I have seen hundreds of students master this.

The trick is not to do the math in your head every time you speak, but to simply memorize the “sound” of the numbers as if they were unique vocabulary words.

In this guide, I’ll break down exactly how it works so you can start counting today.

The easy numbers (0-19)

Before we get into the complicated math of the higher numbers, let’s look at the basics.

The numbers from 0 to 12 are unique words that you just need to memorize. If you know English or German, many of these will sound familiar to you.

From 13 to 19, the pattern is very standard. You simply add the suffix -ten (similar to “-teen” in English).

• 13: Tretten
• 14: Fjorten
• 15: Femten
• 16: Seksten (pronounced like “sais-den”)
• 17: Sytten
• 18: Atten
• 19: Nitten

The “ones before tens” rule

Once you hit the number 20, you need to learn the golden rule of Danish counting.

In English, we say “Twenty-one” (Tens + Ones). In Danish, we say “One-and-twenty” (Ones + Tens).

This is exactly the same as in German or Dutch. You state the unit digit first, then the word og (and), and finally the ten digit.

So, 21 is not tyve-en. It is enogtyve (one-and-twenty).

Here are a few examples to help you see the structure:

• 22: Toogtyve (Two-and-twenty)
• 35: Femogtredive (Five-and-thirty)
• 48: Otteogfyrre (Eight-and-forty)

The logic behind 50, 70 and 90

This is the part that usually scares beginners.

As I mentioned in the introduction, Danish uses a Base-20 system.

In the old days, numbers were counted in “scores” (groups of 20).

• 60 is 3 x 20.
• 80 is 4 x 20.

In modern Danish, we have shortened these words, so you don’t really hear the “times twenty” part anymore, but it helps to know the history to understand the spelling.

For example, the number 60 used to be tresindstyve (three times twenty). Today, we just say tres.

But what about 50, 70 and 90?

This uses a concept involving “half”. When a Dane says “half three” (halvtredje), in the context of numbers, they historically meant “halfway to the third score”.

If you have the first score (20) and the second score (20), and you are halfway to the third score (10), you have 50.

• 50 is halvtreds (Short for halvtredsindstyve -> Halfway to the third x 20).
• 70 is halvfjerds (Short for halvfjerdsindstyve -> Halfway to the fourth x 20).
• 90 is halvfems (Short for halvfemsindstyve -> Halfway to the fifth x 20).

Does your head hurt?

Don’t worry. As a learner, you do not need to do this math in your head. Native speakers certainly don’t! To them, halvtreds just means 50.

My advice is to ignore the math and just memorize the vocabulary list in the next section.

The tens (decades) cheat sheet

Here is the essential table you need to memorize.

Note that 20, 30 and 40 are distinct and don’t strictly follow the “score” rule in the same way the higher numbers do, which makes them easier to remember.

When you combine these with single digits, remember the “Ones before Tens” rule.

Ordinal numbers (1st, 2nd, 3rd…)

You will often need ordinal numbers to talk about dates (like the 1st of May) or which floor an apartment is on (Danes live in apartments a lot).

The good news is that these are much easier than the cardinal numbers because you don’t have to combine them in weird ways.

For numbers above 10, strictly speaking, you add -ende to the number, but usually, we just use the number itself or write it with a dot.

For example, to say “The 20th of April”, we write den 20. april and say den tyvende april.

How to actually learn this without headaches

I know the theory of 50 being “2.5 x 20” is interesting, but it is not helpful when you are standing in a supermarket in Copenhagen trying to pay for your groceries.

Here is my best advice for second language acquisition regarding numbers:

1. Stop translating and calculating.

When you hear halvtreds, don’t think “half three times twenty.” Train your brain to immediately see the number 50. Flashcards are excellent for this.

2. Listen to prices.

Next time you are in a Danish shop (or watching a Danish show), listen intently for the prices. Prices are the most common way numbers are used naturally.

3. Focus on the “Halvs”.

The numbers 50, 70, and 90 all start with halv. The numbers 60 and 80 do not. If you hear halv-, you know it’s an odd number (5, 7, 9). That cuts your options in half immediately!

Learning the Danish numbers takes a little bit of patience, but once you get the rhythm of saying the “ones” before the “tens,” it becomes second nature.

Held og lykke! (Good luck!)