messen
to measure
To determine the size, quantity, temperature, or another property of something using a measuring device or a scale.
Der Arzt hat meinen Blutdruck gemessen.
The doctor measured my blood pressure.

to measure
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to measure
To determine the size, quantity, temperature, or another property of something using a measuring device or a scale.
Der Arzt hat meinen Blutdruck gemessen.
The doctor measured my blood pressure.

The verb 'messen' (to measure) has two main uses. It either describes an active action (a person measures something) or a static state (a thing has a certain size).
Der Handwerker misst die Breite der Tür.
The tradesperson measures the width of the door.
In the meaning 'to determine a property', 'messen' (to measure) is often combined with medical or physical quantities. Typical examples are: 'Fieber messen' (to take someone’s temperature), 'den Blutdruck messen' (to measure blood pressure), 'die Temperatur messen' (to measure the temperature), or 'die Geschwindigkeit messen' (to measure speed).
Die Krankenschwester kommt gleich, um bei Ihnen Fieber zu messen.
The nurse will be here in a moment to take your temperature.
In the meaning 'to compare oneself', the verb is reflexive and is always used with the preposition 'mit' and the dative: 'sich mit jemandem/etwas messen' (to compete with someone/something).
Der junge Läufer möchte sich mit den besten Athleten der Welt messen.
The young runner wants to compete with the best athletes in the world.
When 'messen' (to measure) is used in the sense of 'to judge', it takes the preposition 'an' and the dative. The structure is: 'jemanden/etwas an etwas (Dativ) messen' (to judge someone/something by something).
Man sollte Menschen nicht nur an ihrem Erfolg messen.
You shouldn’t judge people only by their success.
to count
'zählen' and 'messen' are both used when you want to get exact information about an amount or size. 'zählen' fits when there are individual things or people and you want to know how many there are. 'messen' fits when you determine a property, for example length, temperature, weight, or time, often with a device. The words can be confused because both produce a result with numbers. The difference is: you count individual items, but you measure properties such as height, width, or temperature.

Die Ärztin misst die Temperatur, weil das Kind seit gestern Fieber hat.
The doctor measures the temperature because the child has had a fever since yesterday.
Bitte zähl die Stühle, damit wir wissen, ob alle Gäste einen Platz haben.
Please count the chairs so we know whether all the guests have a seat.