die Empfindung
sensation
A physical perception conveyed through the senses, such as cold, warmth, pain, or touch.
Nach der Betäubung hatte er keine Empfindung mehr im Bein.
After the anesthesia, he no longer had any sensation in his leg.

sensation / feeling
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sensation
A physical perception conveyed through the senses, such as cold, warmth, pain, or touch.
Nach der Betäubung hatte er keine Empfindung mehr im Bein.
After the anesthesia, he no longer had any sensation in his leg.

'Die Empfindung' (sensation/feeling) is the noun corresponding to the verb 'empfinden' (to feel or perceive). If you know that 'empfinden' means 'fühlen' (to feel) or 'wahrnehmen' (to perceive), you can understand the meaning of the noun more easily.
Er konnte seine Empfindungen nur schwer in Worte fassen.
He found it difficult to put his feelings into words.
You can recognize the meaning from the context: If it is about the body, senses, or medicine, a physical sensation is meant. If it is about intuition, feelings, or a hunch, an inner feeling is meant.
Er spürte eine schmerzhafte Empfindung im Rücken.
He felt a painful sensation in his back.
For physical perception, 'Empfindung' (sensation) is often combined with adjectives such as 'kalt' (cold), 'warm' (warm), 'taub' (numb), or 'brennend' (burning). The phrase 'eine Empfindung von Kälte/Wärme' (a sensation of cold/warmth) is also common.
Nach dem langen Spaziergang im Schnee hatte sie eine taube Empfindung in den Zehen.
After the long walk in the snow, she had a numb sensation in her toes.
To express an inner feeling or a hunch, the fixed structure 'die Empfindung haben, dass ...' (to have the feeling that ...) is often used. It is followed by a subordinate clause.
Ich habe die Empfindung, dass wir hier nicht willkommen sind.
I have the feeling that we are not welcome here.
feeling / sense
'das Gefühl' and 'die Empfindung' can both describe something you perceive internally or physically. 'Gefühl' is very common in everyday language and is especially suitable for emotions or a hunch. 'Empfindung' sounds somewhat more precise or formal and is often used for physical sensations such as warmth, pain, or touch. However, it can also mean an inner perception. The words can be confused because both can be used for emotional and physical experience. If you are talking about love, fear, or a gut feeling, 'Gefühl' usually sounds more natural. For pain, cold, or touch, 'Empfindung' is often more precise.

Beim Arzt beschrieb ich eine leichte Empfindung von Kälte im linken Arm.
At the doctor's office, I described a slight sensation of cold in my left arm.
Ich habe das Gefühl, dass heute noch etwas Wichtiges passiert.
I have the feeling that something important is still going to happen today.