They both are translated as result, but it seems that their language use is not the same. Can somebody explain their proper use?
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I'm a native speaker and it's actually not that difficult, even though they are quite similar.
While "die Folge" is more like the consequence (so something that follows which doesn't finish it completely, like a secondary result I guess), the word "das Ergebnis" is more like a (final) outcome which finishes (for example a research) completely.
I'd like to add that Folge has multiple meanings, e.g. episode (of TV series), sequence (math), ... Basically it's something that follows in some way.
Note the similarity of Folge and follow. This is not coincidence but due to a common etymology. The Old English folgian only later became follow.
IMHO "Folge" (in the result-like sense) emphasizes causality or a similarly strong link.
Ergebnis is often more specific, e.g. you'd say that things falling towards the center of earth is die Folge of the law of gravity. Whereas the Ergebnis of some calculation is 42. If you want to emphasize that the result is obtained by a logical sequence of thoughts:
in that case, you can also say
You can describe situations where the result "happens", independent of which of a number of theoretically possible alternatives is actually right:
As a native speaker I would say that Ergebnis is a final thing and Folge means that something happens after something was done or happened.
If you say "Das Ergebnis von 1+1 ist 2.", then this is a final result.
It's really hard to explain, because these words are very similar, but I hope this helped a bit.
is mostly used to illustrate negative, unwanted consequences. If you look up "Folge" in the Duden, you will notice that all (!) examples under the relevant first meaning are of negative consequences:
There is not one example of positive consequences!
I would say that "result" is not a good translation of "Folge". I think "consequences" is better.
describes the final outcome or result in a more neutral manner. "Ergebnisse" can be both negative or positive:
Please note that both "Folge" and "Ergebnis" have other meanings beside "result/consequences". I did not mention them here since they don't pertain to your question.
I think "Ergebnis" is used mainly for intended consequences/results, while "Folge" is used more for unintended consequences (which may explain what's observation that it is most often used for negative consequences: Usually negative consequences are unintended, while people like to claim positive consequences of their actions as intended, even if they didn't really foresee them).
An example of a positive use of "Folge" where I would not say "Ergebnis":
On the other hand, the following use of "Ergebnis" is for a quite negative result, but I'd nevertheless consider it preferable to "Folge":
However the next sentence might be:
Here, again, I think "Ergebnis" wouldn't fit because the person running amok most probably didn't intend the security measures to be made stricter.
Vorsicht vor falschen Dichotomien!
Wie so oft versuchen die Teilnehmer einen Unterschied in die Bedeutung der Wörter hineinzugeheimnissen, der dort nicht ist.
Es gibt in Ursache-Wirkungs-Beziehungen die Wirkung sowohl als Ergebnis als auch als Folge. Ein Unterschied existiert da nicht. Es gibt vorläufige Ergebnisse, und auch endgültige Ergebnisse sind Folgen.
Wenn ein Ereignis nur später, aber nicht Wirkung war, ist es weder Folge noch Ergebnis.
Nur bei mathematischen Gleichungen nennt man eine angestrebte Vereinfachung Ergebnis, nicht Folge, wie Eric richtig schrieb, und NoAnswer hat richtig herausgestellt, dass Folge auch Episode oder Sequenz bedeuten kann.