Я по-настоящему рад, что мы помирились.

Because рад agrees with я, which is singular.

• рад = masculine singular
• рада = feminine singular
• рады = plural

So:

• Я рад = I am glad (said by a man)
• Я рада = I am glad (said by a woman)
• Мы рады = We are glad

In this sentence, the speaker is one person, so the singular form is used.

Рад is the short form of the adjective радостный? Not exactly in meaning, but grammatically it behaves like a short-form adjective.

In Russian, рад / рада / рады is the normal way to say glad in sentences like this:

• Я рад
• Она рада
• Мы рады

It is used predicatively, meaning it functions like the main description in the sentence, similar to am glad in English.

You would not usually say Я радостный to mean I’m glad. That would sound more like I’m cheerful / joyful by nature or at the moment, not specifically glad about something.

Russian usually leaves out to be in the present tense.

So English I am glad becomes simply:

• Я рад

This is completely normal. The idea of am is understood.

Compare:

• Я студент = I am a student
• Она дома = She is at home
• Мы рады = We are glad

In the past or future, forms of быть can appear, but not normally in the present.

По-настоящему means really, truly, genuinely, or for real.

In this sentence, it intensifies рад:

• Я рад = I’m glad
• Я по-настоящему рад = I’m really / genuinely glad

It is hyphenated because that is the standard spelling of this adverb.

This word often gives a stronger, more sincere feeling than just очень. Compare:

• Я очень рад = I’m very glad
• Я по-настоящему рад = I’m genuinely glad

So по-настоящему emphasizes sincerity, not just degree.

Because что мы помирились is a subordinate clause.

The main clause is:

• Я по-настоящему рад

The subordinate clause explains what the speaker is glad about:

• что мы помирились

Russian normally separates this kind of clause with a comma:

• Я рад, что...
• Я думаю, что...
• Я знаю, что...

So the comma is required.

Что means that and introduces the content of what the speaker is glad about.

So:

• Я рад, что мы помирились = I’m glad that we made up

This is very common after words expressing feelings, thoughts, speech, or knowledge:

• Я думаю, что... = I think that...
• Я знаю, что... = I know that...
• Я счастлив, что... = I’m happy that...

In English, that is often optional, but in Russian что is normally stated.

This is about aspect.

• мириться = imperfective
• помириться = perfective

The verb помириться means to make up / reconcile, focusing on the completed result.

So мы помирились means:

• we made up
• we got reconciled
• we are now on good terms again

If you used мирились, it would suggest an ongoing, repeated, or process meaning, such as we were trying to make peace or we were making up, depending on context.

Here the speaker is glad about the completed fact, so perfective помирились is the natural choice.

The -сь is the reflexive ending (a variant of -ся after vowels).

In помириться, it does not literally mean oneself in the English sense. Here it helps form the verb meaning to reconcile / make up with each other.

So:

• мирить = to reconcile someone
• мириться = to reconcile, to make peace, often with each other or with someone

With мы, the meaning is naturally reciprocal:

• мы помирились = we made up (with each other)

So the reflexive form is essential to the meaning of the verb.

Because the reconciliation happened earlier, and the speaker is glad now about that completed event.

Russian often uses the past tense in the subordinate clause to refer to something that has already happened:

• Я рад, что ты пришёл = I’m glad you came
• Я счастлива, что мы встретились = I’m happy that we met
• Я по-настоящему рад, что мы помирились = I’m really glad that we made up

So the emotion is present, but its cause is a past event.

Yes, in many contexts it can.

Russian often drops subject pronouns when they are clear from context. So you may hear:

• По-настоящему рад, что мы помирились.

This can still mean I’m really glad that we made up, especially in conversation.

However, including Я can make the sentence:

• clearer,
• more neutral,
• or slightly more emphatic.

So both are possible, but Я по-настоящему рад... is a perfectly natural full sentence.

In this sentence, it most naturally means we made up with each other.

Because the subject is мы, the reflexive verb помирились is understood reciprocally: both people stopped being in conflict and reconciled.

With other constructions, the verb can work differently:

• Я помирился с братом = I made up with my brother
• Они помирились = They made up
• Она помирилась с ситуацией can mean She came to terms with the situation in some contexts

But with мы помирились, the usual meaning is straightforwardly we reconciled / we made up.

Yes, absolutely.

• Я очень рад, что мы помирились = I’m very glad that we made up
• Я по-настоящему рад, что мы помирились = I’m genuinely / truly glad that we made up

The difference is in nuance:

• очень emphasizes degree: very glad
• по-настоящему emphasizes sincerity/authenticity: genuinely glad

Both are natural. In some contexts, по-настоящему can sound a bit more heartfelt.

It breaks down like this:

• по- = prefix
• мир / мирить = root related to peace/reconciliation
• -и- = verb-forming element
• -л- = past tense marker
• -и = plural ending
• -сь = reflexive ending

So помирились is the past tense, plural, reflexive, perfective form of помириться.

Because the subject is мы, the plural past form is used.

The standard stress is:

• Я по-настоя́щему рад, что мы помири́лись.

A few key points:

• по-настоя́щему has the stress on -я́-
• рад is stressed on the only vowel
• помири́лись has the stress on -ри́-

Stress matters in Russian, so it is worth learning these together with the words.