My shortest was 10 km and came from abroad:
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If you look at distance parameter at postcrossing, then I have several shortest at 37 km, which is distance between center of closest city and my city (even though they might have been shorter, big Moscow starts about 21 km from my city)
Mine is 313 km. I already thought that was short but looking at this thread I am really impressed with how close some addresses were.
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Sent:
Received:
My shortest distance was 8 km - probably shorter in reality, given where I live within my city.
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63 km
But I also had an āinofficial officialā card with a distance of ~ 1 km.
An official card for another Postcrosser landed in my mailbox and the street was just one corner and then about 900 m away and so I did (once again) the delivery 
Just about one or two weeks ago.
163 km, from Belgium to the Netherlands.
Only 20 km!.
It was a postcard I sent to another postcrosser inside Community of Madrid. Not same city, but same province.
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This is the closest sent card, 102 miles.
Sent 22 km from AT to DE
Received 85 km from DE to AT. One can see the town I grew up in on that card actually, and as kid it was common to travel to the senderās city for shopping.
Do kms really change when senders move? Seems like a lot of work for the software, with possible results of km0 even if a sender moves to a city they sent to already.
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In the early days of Postcrossing, we didnāt exclude exchanging with accounts on the same location, plus the granularity of the locations in our database was much sparser, so thereās actually many postcards where the distance āisā 0kms, even when distances could be big! 
These days we keep the senderās and receivers location at time of generating the Postcard ID, so if any of them moves after that, the travelled distance doesnāt change.
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The shortest distance to me is 2800 km from New Zealand and the shortest Iāve sent is 6300 km to Malaysia. Australia is a long way from anywhere!
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My shortest distance is 19 km. (actually there is 8 km.)
From SWAP I received a postcard from a neighboring street - this is less than 1 kilometer.
My shortest official
sent:
received:
So glad to have some company here! My shortest distance so far is some 6600km to Taiwan. I have the within own country option ticked but donāt expect to actually draw an Australian address any time soon.
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On the official PC website, my shortest distance was 113 miles sent in 2016. It no longer has an image though, so I included my second shortest, which was 160 miles.
My absolute shortest though was 6 miles. I send cards to my bestie who only lives that far away.
Sent: 58km
Received: also 58km
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When I lived in Aachen I sent a card to NL that travelled 11km
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The shortest distance Iāve ever sent a card was 193 miles; just one state away from me. However, I did send a card to an address less than 1.5 miles from my sonās home in a different state!!