orthography - 有り難う vs 有難う — Is this the same word?

Do both these words mean "thank you"? If both mean thank you why are they spelled differently? Is one more formal than the other?

Answer

Both are different spellings of ありがとう, neither is more formal, although all three spellings may be differentiated by frequency (see below).

ありがとう "thank you" may be derived from ありがたい through sound change; ありがたい is a compound of 有る and 難い.

In forming compounds, the first verb conjugates to the ren'yōkei (= "masu-stem"). In compound verbs, like 有り得る or 押し付ける, this is usually all that happens, but for other compounds the okurigana (hiragana part of the verb) are sometimes omitted, so both 有難い and 有り難い are possible ways of writing the same word. (Here り is the okurigana of 有り.)

There are many other such examples:

• 受け付け = 受付け = 受付 "reception"


• 乗り物 = 乗物 "vehicle"

ありがとう is usually written in hiragana nowadays, but it may be written with kanji, like you suggest.

Here are the frequencies of the different spellings (from Balanced Corpus of Contemporary Written Japanese, via http://nlb.ninjal.ac.jp and http://www.kotonoha.gr.jp/shonagon)

ありがたい 1987 (74%)
有難い　　  350 (13%)

有り難い　  343 (13%)
有りがたい   17 ( 1%)

ありがとう 7090 (93%)
有難う　　  420 ( 6%)
有り難う　  102 ( 1%)
有りがとう    2 ( 0%)

受付　　　 3916 (85%)
受け付け　  633 (14%)

受付け　　   34 ( 1%)
うけつけ　    3 ( 0%)
受け付　　    1 ( 0%)

乗り物　　  470 (79%)
乗物　　　   95 (16%)
のりもの　   16 ( 3%)
乗りもの　   12 ( 2%)

As you can see, 有難う is about four times as common as 有り難う, but ありがとう is by far the most common.