Learn Hardcore Finnish: Tarvitsen viivaimen, kun piirrän suoraa viivaa paperille. - I need a ruler when I draw a straight line on the paper.

Because the -n ending shows the subject, minä is normally dropped in neutral sentences. You only add minä when you want to emphasize it, for example:

Minä tarvitsen viivaimen, en sinä.
I need a ruler, not you.

So Tarvitsen viivaimen is the normal, unmarked way to say I need a ruler.

Why is it viivaimen and not just viivain?

Viivain is the basic dictionary form (nominative singular).
In this sentence, viivaimen is in the genitive/accusative form, because it is a complete object of a complete action.

Nominative singular: viivain (a ruler – subject form)
Genitive / total object: viivaimen (the whole ruler – as a thing you need)
Partitive: viivainta

With verbs like tarvita (to need), when you need “a whole thing” as a definite, countable object, Finnish usually uses the total object form (genitive here):

Tarvitsen viivaimen. – I need a (whole) ruler.
Ostan viivaimen. – I will buy a ruler.

So viivaimen is chosen because it is a total, countable object of a “complete” need, not an ongoing or partial amount of something.

Could you say Tarvitsen viivainta instead of Tarvitsen viivaimen? What’s the difference?

Yes, Tarvitsen viivainta is grammatically possible, but the nuance changes.

Tarvitsen viivaimen.
→ I need a ruler (a specific, whole ruler; you want to have one / get one).
Tarvitsen viivainta.
→ I need (the use of) a ruler / I am in need of a ruler (more like an ongoing, indefinite need, less about one specific object).

In many everyday contexts, Tarvitsen viivaimen is the natural choice when you mean “I need a ruler (for this task)”.
The partitive viivainta sounds more like a general, ongoing state of needing or using a ruler, or is more abstract.

Why is viivain → viivaimen? Where does that extra m come from?

This is just how the noun viivain is inflected; you have to learn its pattern.

nominative: viivain
genitive / total object: viivaimen
partitive: viivainta

The stem of the word alternates between viivai- and viivain- depending on the case:

add -n directly to the nominative stem → viivain + ta → viivainta
but for the genitive, the stem ends in a vowel → viivai- + men → viivaimen

The -men ending is a common way to form genitives of some -in / -ain words (compare: puhelin → puhelimen). So viivain → viivaimen is a regular but slightly non-obvious pattern you must memorize.

Why is there a comma before kun?

In Finnish, you normally put a comma before a subordinate clause, including ones introduced by kun (“when”, “as”, “because” in some contexts).

Structure of the sentence:

main clause: Tarvitsen viivaimen
subordinate clause: kun piirrän suoraa viivaa paperille

Rule: When a kun-clause follows the main clause, you separate it with a comma:

Tarvitsen viivaimen, kun piirrän suoraa viivaa paperille.

If you reverse the order, you still use a comma:

Kun piirrän suoraa viivaa paperille, tarvitsen viivaimen.

So the comma is required by Finnish punctuation rules for main + subordinate clause combinations.

Why is it piirrän and not piirtän or something else?

The verb is piirtää (to draw). It undergoes consonant gradation in the present tense.

infinitive: piirtää
stem: piirtä-
1st person singular ending: -n

But in the present tense, rt often changes to rr in some forms (strong ↔ weak grade alternation). So:

piirtä- + n → piirrän (I draw)
piirtä- + t → piirrät (you draw)

Other forms:

hän piirtää – he/she draws (no change)
me piirrämme – we draw
he piirtävät – they draw

So piirrän is the correct 1st person singular present form, because of rt → rr gradation plus the -n ending.

Why is it suoraa viivaa and not suoran viivan? In English it’s “a straight line”.

This is about the object case again: here Finnish uses the partitive (suoraa viivaa), not the total object (suoran viivan).

suora viiva – a straight line (basic form)
partitive: suoraa viivaa
total object (genitive): suoran viivan

With verbs of drawing, writing, etc., Finnish often uses the partitive object when the action is:

ongoing, uncompleted, or
not referring to a specific, clearly delimited item

Piirrän suoraa viivaa suggests you are in the process of drawing straight line(s), focusing on the activity itself rather than one specific “finished” line.

If you say:

Piirrän suoran viivan.

it sounds more like: “I am (going to) draw one specific straight line (from A to B) and complete it.” It’s more bounded and result-focused.

In everyday speech, piirtää viivaa (partitive) is very natural when talking about drawing lines generally, without highlighting a single, completed line. That’s why the sentence uses suoraa viivaa.

Why are both suoraa and viivaa in the same form? Do adjectives always copy the noun’s case?

Yes. In Finnish, adjectives normally agree with the noun in:

case
number
(and sometimes) possessive suffixes

Here:

noun: viiva → partitive singular viivaa
adjective: suora → partitive singular suoraa

So you get:

suoraa viivaa – straight line (partitive singular)
suoran viivan – straight line (genitive singular / total object)
pitkiä viivoja – long lines (partitive plural)
uuteen taloon – into a new house (illative singular)

So yes, suoraa matches viivaa in case and number, as is normal in Finnish.

Why is it paperille and not paperilla or paperiin?

Finnish has different local cases for “on”, “onto”, “in”, “into”, etc. Here:

paperilla (adessive) = on the paper (static location)
paperille (allative) = onto the paper (movement onto a surface)
paperissa (inessive) = in the paper (inside it)
paperiin (illative) = into the paper (movement into the inside)

In this sentence you are drawing a line onto the surface of the paper, so movement onto a surface is expressed with -lle:

piirtää viivaa paperille – to draw a line onto (the) paper
later you could say:
Viiva on paperilla. – The line is on the paper. (now static, so -lla)

Paperiin would suggest going into the material itself (e.g. something soaking into the paper), which is not what is meant here. That is why paperille is used.

Why is paperille singular? In English we just say “on paper” without “a” or “the”.

Finnish does not have articles (a/an, the), and it also typically uses the singular for these generic “on paper / in water / on glass” types of expressions.

paperille – onto (the) paper / onto paper
paperilla – on (the) paper / on paper

So paperille on its own can mean:

onto the paper (a specific sheet just mentioned), or
onto paper in a more general sense

You don’t need (and can’t add) an article-like word. The context tells you whether it’s more like “onto a sheet of paper” or “onto paper (in general)”.

Could the word order be Kun piirrän suoraa viivaa paperille, tarvitsen viivaimen? Is that different?

Yes, that word order is perfectly correct:

Tarvitsen viivaimen, kun piirrän suoraa viivaa paperille.
Kun piirrän suoraa viivaa paperille, tarvitsen viivaimen.

Both mean the same thing. Finnish word order is relatively flexible, especially with clauses like this.

Placing the kun-clause first (Kun piirrän…) can slightly emphasize the condition/time:

When I draw a straight line on paper, (then) I need a ruler.

Placing it second keeps the focus first on the fact that you need a ruler, and only then explains in which situation. But in everyday usage, the difference is small; both are natural.

Why doesn’t Finnish say a ruler / a straight line? Where are the articles?

Finnish simply has no articles like English a/an or the.

viivain / viivaimen can mean a ruler or the ruler, depending on context.
suoraa viivaa can mean a straight line or the straight line, again from context.

So:

Tarvitsen viivaimen, kun piirrän suoraa viivaa paperille.
= I need a ruler when I draw a straight line on paper.
or in another context possibly
= I need the ruler when I draw the straight line on the paper.

There is no word corresponding to a or the; you infer that from the situation and from previous references in the conversation.