What is the difference between nachvollziehen and verstehen? In my dictionary they both mean “to comprehend”. Do they have a big difference in usage?
If you are either able to retrace or to reconstruct something or able to follow someone, then you can use nachvollziehen. If, however, it's just about understanding and comprehension of the nature of something, you can only use verstehen.
Both words have an overlapping sense but verstehen is a little broader in meaning. You can use verstehen when you are able to hear someone, as in Can you hear me?:
Kannst du mich verstehen?
Or if you didn't understand someone, then you say:
Ich kann dich (akustisch) nicht verstehen.
Apart from that, verstehen is basically used in the sense of to understand the meaning or significance of something. Examples:
- Die Bedienungsanleitung versteht kein Mensch.
- Unterschreiben Sie nichts, was Sie nicht verstehen.
- Ich kann nicht verstehen, wie man so viel Glück auf einmal haben kann.
- Ich verstehe nicht, warum es dir so wichtig ist.
- Ich verstehe sehr gut, dass ...
Nachvollziehen is synonymous to verstehen in many contexts. I think there's a simple way to find out if that is true. This is actually already mentioned in the other answer, I will just put it in another way again.
The meaning of nachvollziehen is to retrace or to reconstruct something in mind. Example: If you are able to retrace the feelings someone has when someone close to them died, you can say1:
Ich kann sehr gut nachvollziehen, was du durchmachst.
Another example: Your math teacher explains how to solve an equation and you are not able to follow him, i.e. how to get from, e.g., step 3 to step 4, you can say:
Ich kann nicht ganz nachvollziehen, wie man von Schritt 3 zu Schritt 4 kommt.
In both example you can still go with verstehen though.
1: I am aware that you hardly ever will be able to fully understand what someone is feeling in such a moment; it's just an example to make my point.
"Nachvollziehen" and "verstehen" both are very similar in meaning (as you already found out), but there are some subtle differences that I want to emphasize here.
At first you don't understand the reasoning behind someones decision and they explain it to you. You then do understand the chain of thoughts that let to that decision.
Here, you'd rather use "nachvollziehen".
"Verstehen" is valid here as well, but doesn't carry the deductive meaning.
Das kann ich nachvollziehen".
Das ist nachvollziehbar.
If you're unable to understand something for technical reasons, like acoustic failure or irritating noises, it would be wrong to use "nachvollziehen".
Wie bitte? Das habe ich nicht verstanden.
Since the word "nachvollziehen" refers basically to the brain-action of understanding something instead of the ear-action (yes, my English is awesome today), you usually don't negate it in the standard way: Use
Das kann ich nicht nachvollziehen.
*Das habe ich nicht nachvollzogen.
These details are kinda specific, so you should be fine with using both words synonymously in (most?) other places. When in doubt, use "verstehen" since it's more common.
There is also one practical detail about the difference between the two.
When there is a discussion going on and somebody replies to what another person says starting with "Das (what you say) kann ich nachvollziehen" instead of "Das kann ich verstehen" it can be a very diplomatic way to introduce a contrary opinion. Because "Das kann ich nachvollziehen" implies that although you don't really agree with him you perfectly understood why he thinks that way which lends your following contrary statement more substance. If you would have said "Ich kann das verstehen" it somehow implies to a little extent that you AGREE with his view, you agree to his thoughts in that context he explains while nachvollziehen is more UNDERSTAND his thoughts.
But the difference is still very tiny..
Nachvollziehen means to comprehend a complex situation by retracing it step by step from beginning to end until you get how this situation or outcome appeared.
Verstehen means just that you got it. Usually without having to retrace the steps. Because the thing to understand was less complex or in other words simple enough to get / understand without having to get a long explanation.
Or you had similar experience and "knew" the steps already. But then if it is complex, you can "nachvollziehen"; if it is simple, you just "verstehen".
Although far less technical than the other answers, I think of the English slang phrase "I'm picking up what you're putting down." If that phrase works better than "I understand", then you nachvollziehen is more appropriate. Again, not nearly as scientific as the explanations above, but it seems to work fairly well.