Нужно определить точную сумму.

Because this is an impersonal construction.

Нужно определить точную сумму. literally works like It is necessary to determine the exact amount/sum.

Russian very often uses:

нужно + infinitive

to mean:

• it is necessary to ...
• one needs to ...
• must ... (in a softer, less personal way than a direct command)

So the sentence does not name who must do it. The person is understood from context.

If you wanted to make the person explicit, you could say things like:

• Мне нужно определить точную сумму. = I need to determine the exact amount.
• Нам нужно определить точную сумму. = We need to determine the exact amount.

Here нужно is a predicative word meaning necessary / needed.

In learner terms, it behaves like a word used in impersonal sentences rather than like a normal adjective directly describing a noun.

So in:

Нужно определить точную сумму.

нужно does not mean needed in the sense of describing a noun like a needed thing. Instead, it means:

• it is necessary
• it is needed

This is very common in Russian:

• Нужно работать. = It is necessary to work.
• Нужно подождать. = We need to wait.

Because определить is perfective, while определять is imperfective.

Russian verb aspect matters a lot. Here:

• определять = to be determining / to determine in a process, generally or repeatedly
• определить = to determine, with emphasis on reaching the result

In this sentence, the idea is to arrive at the exact sum, so the perfective verb определить is natural.

Compare:

• Нужно определить точную сумму. = We need to determine the exact sum.
  (focus on getting the result)

• Нужно определять точную сумму в каждом случае. = It is necessary to determine the exact sum in each case.
  (more general, habitual, procedural)

It is in the accusative case because it is the direct object of the verb определить.

You are determining what?

точную сумму

That is the thing being determined, so it takes the accusative.

Breakdown:

• точная сумма = nominative, exact sum
• точную сумму = accusative, exact sum as the object

Since сумма is a feminine noun, the accusative singular looks like this:

• adjective: точная → точную
• noun: сумма → сумму

Because in Russian, adjectives must agree with the nouns they describe.

They agree in:

• gender
• number
• case

Here:

• сумма is feminine
• it is singular
• it is in the accusative

So the adjective точный must match that:

• masculine: точный
• feminine nominative: точная
• feminine accusative: точную

That is why the phrase becomes:

точную сумму

not just one word changing by itself.

It can mean either, depending on context, which is why it sometimes confuses learners.

In this sentence, определить means:

• to determine
• to establish
• to work out

So:

Нужно определить точную сумму. = It is necessary to determine the exact sum/amount.

If you were talking about giving a definition in a dictionary or explaining a concept, определить could also mean to define.

So the core idea is to establish exactly what something is.

Yes. In many contexts, надо and нужно are very close.

So you can say:

Надо определить точную сумму.

This also means It is necessary to determine the exact sum.

A rough learner-friendly way to think of them:

• надо = very common in everyday speech
• нужно = also common, sometimes sounds slightly more neutral or formal depending on context

In many sentences, the difference is small.

No, Russian word order is relatively flexible.

The neutral order here is:

Нужно определить точную сумму.

But other orders are possible if you want different emphasis, for example:

• Точную сумму нужно определить.
• Определить точную сумму нужно.

These alternatives can sound more emphatic or context-driven. For a learner, the original order is the safest and most neutral.

The stress is:

Ну́жно определи́ть то́чную су́мму.

A simple pronunciation guide:

• Ну́жно = NOOZH-na
• определи́ть = a-prye-dye-LEET'
• то́чную = TOCH-nu-yu
• су́мму = SOOM-mu

A few helpful points:

• ж sounds like the s in measure
• ч sounds like ch
• the final ть in определить is a soft t sound

No. Сумма can mean:

• a mathematical sum
• an amount of money
• a total amount more generally

So in real life, точная сумма often means:

• the exact amount
• the exact total
• the exact sum

The correct English translation depends on context.

Russian has no articles.

So точную сумму could correspond to:

• the exact sum
• an exact sum
• sometimes just exact sum

Context tells you which is most natural in English.

That is why learners often have to resist the urge to look for a Russian word meaning the or a here—there simply is none.