Ich messe die Höhe.

Because ich needs the 1st person singular form of the verb.

The infinitive is messen = to measure.

Its present-tense forms are:

• ich messe = I measure / I am measuring
• du misst
• er/sie/es misst
• wir messen
• ihr messt
• sie/Sie messen

So in Ich messe die Höhe, messe matches ich.

In the present tense, many German verbs add -e in the ich form.

So:

• messen → ich messe
• machen → ich mache
• lernen → ich lerne

This is a normal conjugation pattern.

Höhe is a feminine noun in German, so its article is die in the nominative singular.

• die Höhe = the height

In this sentence, die Höhe is also the direct object, so it is in the accusative case. For feminine nouns, the accusative article is still die.

So:

• nominative: die Höhe
• accusative: die Höhe

That is why the article does not change.

It is in the accusative case because it is the thing being measured.

The verb messen usually takes a direct object:

• Ich messe die Höhe.
• Er misst die Länge.
• Wir messen den Raum.

A good question to ask is: What am I measuring?
Answer: die Höhe.
That makes it the direct object, so accusative is used.

Because all German nouns are capitalized.

So:

• die Höhe
• das Haus
• der Tisch

Even in the middle of a sentence, nouns begin with a capital letter.

Yes. Höhe is the noun related to the adjective hoch (high / tall).

• hoch = high
• die Höhe = height

This is similar to English high and height, although the word formation is not identical.

You will often see similar pairs in German:

• lang → die Länge = long → length
• breit → die Breite = wide → width
• hoch → die Höhe = high → height

Höhe can be tricky because of the ö and the two syllables.

It is pronounced roughly like:

• HÖ-huh

More precisely:

• the first syllable has ö, a vowel that does not exist exactly in English
• the second e at the end is pronounced as a weak uh sound, not silent

So Höhe has two syllables: Hö-he

Important:

• Do not pronounce it like English hoe
• Do not ignore the final -e

The ö is an umlaut vowel. English does not have an exact equivalent, but one common trick is:

1. Say ee as in see
2. Keep your tongue in that position
3. Round your lips as if saying o

That gets you close to ö.

This sound appears in many German words:

• schön
• können
• Höhe

Yes. It is in the present tense, and German present tense often covers both of these English meanings:

• I measure the height
• I am measuring the height

German does not need a separate progressive form like English am measuring.
So Ich messe die Höhe can mean either one, depending on context.

This is the normal German main clause word order:

• subject: Ich
• verb: messe
• object: die Höhe

German main clauses usually place the conjugated verb in the second position.

So this sentence follows the basic pattern very neatly: Subject + verb + object

In general, die can mean either:

• the for a feminine singular noun
• the for a plural noun

But here it is clearly feminine singular, because Höhe is singular.

So:

• die Höhe = the height
• die Höhen = the heights

This is a stem-changing verb.

The infinitive is messen, but in the du and er/sie/es forms, the vowel changes from e to i:

• ich messe
• du misst
• er/sie/es misst

This is something learners just have to remember for certain verbs.

So ich messe is correct, even though du misst looks different.

Yes, it is natural and grammatically correct.

It sounds like something you would say in a practical or technical context, for example:

• measuring a building
• measuring a table
• measuring a mountain in a description
• measuring an object in a lab or workshop

In everyday conversation, German speakers might sometimes add more detail, such as what object the height belongs to:

• Ich messe die Höhe des Schranks. = I’m measuring the height of the cabinet.
• Ich messe die Höhe von dem Regal. = I’m measuring the height of the shelf.

But the shorter sentence by itself is perfectly fine.