Ich fahre mit dem Rad in die Stadt.

Because mit always takes the dative case in German.

• Base noun: das Rad
• Dative form: dem Rad

So:

• mit dem Rad = by bike / with the bike

This is a very common pattern:

• mit dem Auto
• mit dem Zug
• mit dem Bus

The article changes because of the preposition mit, not because the meaning changes.

Rad is a very common short form of Fahrrad.

So these are both normal:

• mit dem Rad
• mit dem Fahrrad

In everyday speech, Rad is often more natural and concise. It usually clearly means bicycle from the context, even though Rad literally can also mean wheel in other situations.

Because this sentence describes movement toward a destination.

The preposition in is a two-way preposition, which means:

• accusative for movement/change of location
• dative for location/static position

So:

• in die Stadt = into the city / to town → movement, so accusative
• in der Stadt = in the city → location, so dative

Compare:

• Ich fahre in die Stadt. = I am going into town.
• Ich bin in der Stadt. = I am in town.

In this sentence, fahren means something like to go / travel / ride using a vehicle or something you ride.

It is used for transportation such as:

• Auto fahren = drive a car
• mit dem Zug fahren = go by train
• Rad fahren = ride a bike

So in Ich fahre mit dem Rad in die Stadt, fahre does not necessarily mean drive in the English sense. With a bicycle, it means ride or go by bike.

Because fahre is the 1st person singular form of fahren.

The verb fahren is conjugated like this in the present tense:

• ich fahre
• du fährst
• er/sie/es fährt
• wir fahren
• ihr fahrt
• sie/Sie fahren

So with ich, the correct form is fahre.

Because Rad is a noun, and in German all nouns are capitalized.

That is why you see:

• das Rad
• die Stadt

But verbs and prepositions are not capitalized here:

• fahre
• mit
• in

This is one of the most noticeable spelling differences between German and English.

Yes, the order can be different, but this version is very natural.

German often places sentence elements in a flexible way, especially after the verb. In neutral statements, details often appear in an order like:

• time
• manner
• place/destination

Here, mit dem Rad describes the manner/means of transport, and in die Stadt gives the destination.

So this order sounds natural:

• Ich fahre mit dem Rad in die Stadt.

You may also hear:

• Ich fahre in die Stadt mit dem Rad.

That is grammatically possible, but it sounds less neutral in many contexts. The original sentence is the most standard everyday phrasing.

Yes, but it is a slightly different structure.

German has the common expression:

• Fahrrad fahren or Rad fahren = to ride a bike

So these are both possible:

• Ich fahre mit dem Rad in die Stadt.
• Ich fahre Rad in die Stadt.

The version with mit dem Rad emphasizes the means of transport a bit more.
The version with Rad fahren treats it more like the activity to cycle.

Both are normal.

Because gehen means to walk or sometimes to go in a very general sense, but not when you are traveling by bike.

So:

• Ich gehe in die Stadt. = I walk to town.
• Ich fahre mit dem Rad in die Stadt. = I go to town by bike.

When a vehicle or rideable transport is involved, German usually uses fahren, not gehen.

Not necessarily. In German, in die Stadt often means into town or to the city center, even when no specific city is being identified.

So die Stadt can refer to:

• the city in general
• town, from the speaker’s point of view
• the town center / urban area

This is similar to English going into town, where the town does not always mean one clearly named place.

Yes, per Rad exists, but it is less common in everyday speech.

Compare:

• mit dem Rad = the most natural everyday expression
• per Rad = understandable, but often a bit more formal, written, or stylistic

For a learner, mit dem Rad is the safest and most common choice.

Yes.

• mit dem Rad means by bike and focuses on the means of transport.
• auf dem Fahrrad literally means on the bicycle and focuses more on physical position.

So:

• Ich fahre mit dem Rad in die Stadt. = I go to town by bike.
• Ich sitze auf dem Fahrrad. = I am sitting on the bike.

You can say auf dem Fahrrad in some contexts, but for normal by bike meaning, mit dem Rad is much more idiomatic.