
spüren
to feel
To perceive something physically, for example through the skin or other senses.
Ich spüre die Sonne auf meinem Gesicht.
I feel the sun on my face.
to feel / sense
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to feel
To perceive something physically, for example through the skin or other senses.
Ich spüre die Sonne auf meinem Gesicht.
I feel the sun on my face.

to sense
To intuitively perceive a feeling, a hunch, or an atmosphere.
Man konnte die Anspannung im Raum förmlich spüren.
You could almost physically sense the tension in the room.

to feel
To experience the effects or consequences of something.
Die kleinen Geschäfte spüren die Konkurrenz durch den Online-Handel deutlich.
Small shops are clearly feeling the competition from online retail.
'Spüren' (to feel/sense) is related to the noun 'die Spur' (the track/trace). Originally, it meant to follow a trail. Today it describes perceiving something that is not always directly visible, as if one were following a track.
Der Jäger spürte das Wild im Wald auf.
The hunter tracked down the game in the forest.
'Spüren' is usually used with an accusative object that describes what one feels. However, it can also be used with a subordinate clause with 'dass' or with an infinitive construction to express a more complex perception.
Ich spüre einen leichten Schmerz im Rücken.
I feel a slight pain in my back.
For physical perceptions, 'spüren' is often combined with sensory impressions: 'die Wärme spüren' (to feel the warmth), 'den Wind spüren' (to feel the wind), 'den eigenen Herzschlag spüren' (to feel one's own heartbeat), or 'einen Stich spüren' (to feel a sharp pain/sting).
Nach dem langen Spaziergang spürte er seine Füße kaum noch.
After the long walk, he could hardly feel his feet anymore.
For intuitive perceptions, 'spüren' is connected with emotions or atmospheres: 'die Angst spüren' (to sense fear), 'die Freude spüren' (to sense joy), 'eine Veränderung spüren' (to sense a change), or 'die Anspannung spüren' (to sense the tension).
Obwohl niemand etwas sagte, konnte man die Nervosität im Raum spüren.
Although no one said anything, you could sense the nervousness in the room.
When referring to consequences, 'spüren' is often used in economic or social contexts: 'die Folgen spüren' (to feel the consequences), 'die Auswirkungen spüren' (to feel the effects), or 'den wirtschaftlichen Druck spüren' (to feel the economic pressure).
Die Bevölkerung spürt die Auswirkungen der neuen Politik.
The population is feeling the effects of the new policy.
to feel
For a physical stimulus, both fühlen and spüren can be used. Fühlen focuses more on the physical sensory experience, while spüren often emphasizes consciously noticing the stimulus. The difference is a nuance, not a fixed distinction.

Plötzlich spüre ich die Wärme der Tasse an meinen Händen.
Suddenly, I feel the warmth of the cup on my hands.
Ich fühle die Wärme der Tasse an meinen Händen.
I feel the warmth of the cup on my hands.