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Both words can be translated as "approximately".

Is there any rule/guidance as to the usage of circa and ungefähr?

I have heard circa being used more often and when there are numbers involved (and particularly when dates are involved).

Please give some examples to clarify the difference or similarity.

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up vote 10 down vote accepted

Ungefähr has approximately three times more entries than circa in a corpus (Wortschatz-Portal Uni Leipzig).

Circa, zirka and ca. together indeed have more than three times as much entries than ungefähr in a corpus (Wortschatz-Portal Uni Leipzig).

That said, the use of circa is restricted to numbers though. I can't think of any example where it wouldn't sound off, when not referring to any numbers. An example where its usage is incorrect.

*Das ist circa mein Problem.

In this example, in contrast, the word ungefähr fits perfectly.

Other examples for ungefähr:

Das kommt nicht von ungefähr.
Das ist ungefähr das gleiche.
Sie waren ungefähr gleich begabt.
Eine ungefähre Angabe würde genügen.

In any of these examples circa doesn't sound well. However, when referring to a number again, you can take circa even if this number is not mentioned.

Es kamen circa gleich viele Leute.
Er ist circa gleich groß.

Still, I'd tend to use ungefähr in those sentences though.

As a conclusion: the claim that circa is used more often than ungefähr is true. You should remember that circa is restricted to numbers. As ungefähr has a broader area of usages and is still less frequent, I think circa is indeed almost solely used for numbers.
This is in contrast to my original assumption that usages are equally frequent. The corpus proved me wrong on this. Still, this outcome surprises me. I'd be interested into data for colloquial only; unfortunately, I don't know any sources for that.

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Nice explanation and thanks for the link to the Leipzig uni portal. – Amol Gawai May 13 '14 at 11:17
The first example is nonsense: "Das ist ungefähr mein Problem." The second example should be treated separatly as it is a fixed saying. The third and forth example could be used with circa but aren't. The fifth example couldn't be used with circa at all, because circa is an adverb, not an adjective. Sixth and seventh example are like third and forth. – Toscho May 13 '14 at 14:14
@bwoebi: I'm German but I wouldn't write zirka instead of circa. Also I don't think I've ever seen it written that way until today. – Uli Gerhardt May 13 '14 at 15:36
@bwoebi Thank you very much for this hint. You are right. Checking the corpus again, including zirka and ca., showed that this word is far more frequent than ungefähr and I stand corrected. My initial assumption proved wrong. – Em1 May 13 '14 at 17:39
@toscho if you are still on a "circa" wave, "das ist ungefähr mein Problem" is indeed nonsense. But if you imagine a situation where somebody has told a story and finishes this sentence, in the sense of "so ungefähr ist mein Problem" ("this covers the problem, more or less"), it does make sense. I think it is an important case where the two words have different usage, even if it is counted as an idiom. – rumtscho May 13 '14 at 22:40

To my experience Swiss Written German (which is about the same as actual High German just with many specific "Swiss" expressions and no sz) uses "circa" or its short form "ca." way more often than our Northern neighbours do, also as a replacement for "ungefähr":

"Das ist ca. die Stelle." - "That's about the place."
"Das ist ca. die Reaktion, die ich erwartet hatte." - "That's about the reaction I expected."
"Das sind ca. die Leute, die wir brauchen" - "That's about the people we need"

I don't know how interesting this is for you, but I mostly wanted to point out, that it also depends on which German speaking regions you take into account.

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Note that I was proved wrong on my initial assumption. According to the corpus circa is used more often as I thought–even in Germany. –– Interestingly, your first example doesn't sound that bad to me. The other two are an absolute disaster to my ear, although the last one refers to a number (number of people) and should be valid according to my answer. I really get the feeling the use of these words varies a lot depending on the region you're living. – Em1 May 13 '14 at 17:48
I live near swiss border and your answer is helpful to me. Thanks for adding another dimension to the discussion. – Amol Gawai May 14 '14 at 8:36
I think, much of Swiss German sounds horrible to German ears :D Anyways, it's definitely a question of your dialect and therefor the region you come from and live in. All the examples are totally fine to Swiss people, maybe less to other German speakers. The last one by the way doesn't refer to a number of people, but to their quality. My translation is not good, it should be: "That's about the KIND of people we need" :) – Patric Hartmann May 14 '14 at 8:55
Anhören tut sich das alles prima, aber das circa im Schiftlichen abzukürzen, ohne dass es in einem formalen Maßzusammenhang auftaucht, ist ein faux pas. – user unknown May 15 '14 at 11:27
You're right. I was a little hasty and misread that sentence. Then again, however, it's OK that the last example isn't fine to my ears. :) – Em1 May 15 '14 at 11:39

Not sure why nobody quoted the "Duden" which was the "only" official resource of correct German during my school time.

(bei Maß-, Mengen- und Zeitangaben) ungefähr, etwa; Abkürzung: ca.

Looking at most the examples given with "gleich" they all compare something. With comparison you need to use ungefaehr not circa. Circa on the other hand can be used if you give an exact numeric value but allow for "wiggle room" (so the actual value could but doesn't have to be a little bit less or more).

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Just to mention a simple use. Before numbers you can use the German word "ungefähr" or the Latin word circa meaning around and there is no difference.

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