
messbar
measurable
Something that can be recorded and quantified using instruments or numbers.
Der Anstieg der Feinstaubbelastung in der Stadt ist deutlich messbar.
The increase in particulate matter pollution in the city is clearly measurable.
measurable
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measurable
Something that can be recorded and quantified using instruments or numbers.
Der Anstieg der Feinstaubbelastung in der Stadt ist deutlich messbar.
The increase in particulate matter pollution in the city is clearly measurable.

noticeable
Noticeable or clearly perceptible, even if it is not quantified exactly.
Seit dem Trainerwechsel ist eine messbare Verbesserung der Teamleistung zu erkennen.
Since the change of coach, a noticeable improvement in the team's performance can be seen.
The word consists of the verb 'messen' (to measure) and the ending '-bar'. The ending '-bar' with verbs means 'can be ...' and thus forms adjectives. 'Messbar' (measurable) therefore literally means 'can be measured'.
Die Temperaturveränderung ist mit diesem Gerät genau messbar.
The change in temperature is precisely measurable with this device.
'Messbar' (measurable) belongs to the word family of 'messen' (to measure). If you know the verb 'messen' (to measure) and the noun 'die Messung' (the measurement), you can easily work out the meaning of 'messbar' (measurable).
Die Messung ergab einen messbaren Unterschied zum Vortag.
The measurement showed a measurable difference compared with the previous day.
You can recognize the figurative meaning 'spürbar' (noticeable) from the fact that 'messbar' (measurable/noticeable) is combined with abstract nouns such as 'Erfolg' (success), 'Fortschritt' (progress), or 'Verbesserung' (improvement). In that case, it is not about an exact number, but about a clear change.
Nach dem Training war ein messbarer Fortschritt zu sehen.
After the training, noticeable progress could be seen.
noticeable / palpable
Both words can describe an effect that is clearly noticed. Spürbar is the usual choice when someone experiences the effect directly. Messbar is possible here, but sounds more marked and presents the effect more as something that could be expressed in numbers. Spürbar is generally more suitable for a subjective perception.

Nach dem Urlaub war die Erleichterung in der Stimmung der ganzen Gruppe messbar.
After the vacation, the relief was measurable in the mood of the whole group.
Nach dem Urlaub war die Erleichterung bei allen spürbar.
After the vacation, everyone’s relief was palpable.