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Kopfschmerz vs. Kopfweh

While both Kopfschmerz and Kopfweh translate to headache, they are not always interchangeable. The primary difference lies in their level of formality and common usage, with Kopfschmerz being the more standard term and Kopfweh being more colloquial.

Kopfschmerz

A2
This is the standard, more formal, and most common word for a headache, composed of Kopf (head) and Schmerz (pain). It is used in all contexts, including medical, professional, and everyday situations. Its plural form, Kopfschmerzen, is very frequently used, often to describe a single instance of having a headache.
Der Arzt diagnostizierte chronische Kopfschmerzen.
(The doctor diagnosed chronic headaches.)
Wegen starker Kopfschmerzen muss ich den Termin heute leider absagen.
(Due to a severe headache, I unfortunately have to cancel the appointment today.)
Stress ist eine häufige Ursache für Kopfschmerzen.
(Stress is a common cause of headaches.)
Ich wachte mit einem dumpfen Kopfschmerz auf.
(I woke up with a dull headache.)

Kopfweh

B1
This is a more informal and colloquial term for a headache, composed of Kopf (head) and Weh (ache/woe). It is often used in everyday spoken language, particularly in southern Germany, Austria, and Switzerland. It can sound a bit softer or less severe than Kopfschmerz and is frequently used when talking to children, similar to how one might say tummy ache in English.
Ich lege mich kurz hin, ich habe ein bisschen Kopfweh.
(I'm going to lie down for a bit, I have a little headache.)
Mein Sohn klagt über Kopfweh und will nicht in die Schule.
(My son is complaining about a headache and doesn't want to go to school.)
Trink ein Glas Wasser, das hilft oft gegen Kopfweh.
(Drink a glass of water, that often helps against a headache.)
Nach dem lauten Konzert hatte ich ziemliches Kopfweh.
(After the loud concert, I had quite a headache.)

Summary

In short, use Kopfschmerz as the default, standard term in almost any situation, especially in writing, formal settings, or when you want to be precise. Use Kopfweh in casual, spoken conversations, particularly if you want to sound more informal or if you are in a region where it is the more common everyday term. When you need the plural (headaches), Kopfschmerzen is almost always the correct choice, regardless of which singular form you prefer.