Washing hands in a bathroom, or with water that came from a bathroom:

A. Washing hands after using the bathroom and after other impurities:[1]

One who uses the bathroom [or does other actions which requires him to wash hands afterwards in order to get rid of the evil spirit that resides on his hands] is to avoid washing his hands using the water of a bathroom.[2] This applies even if he takes the water outside the bathroom.[3] However, in a time of need one may wash his hands inside a bathroom, and may certainly remove the water from the bathroom to wash outside.[4] This especially applies to the sink of a public bathroom, which is generally in a separate area of the room than the toilets and urinals.[5] Nevertheless, initially one is to dry the hands outside the bathroom.[6] 

B. Netilas Yadayim for bread, or for the morning washing:[7]

Water from the sink:[8] One is to avoid washing his hands for the morning washing, or for bread, using a bathroom sink.[9] However, in a time of need, one may wash his hands inside a bathroom on behalf of the morning washing, or to eat bread.[10] In such a case, one is to only wash his hands in the bathroom, however the saying of the blessing and the drying of his hands is to take place outside the bathroom.[11] In all cases, if one is able to bring the water of the bathroom to outside the bathroom, then one is to do so and wash there.[12] However, initially, one is not to wash with water from the bathroom sink even if he brings it outside.[13]

Toilet water:[14] The above leniency is only with regards to sink water. However, toilet water is invalid for washing hands even if it is clean. [The same applies for any water that has remained in the bathroom for a considerable amount of time and is considered repulsive by people.[15]]

C. Does spreading a sheet between the toilet and sink validate the sink to be used for washing?[16]

If the sheet cannot be moved with the wind, and is within three Tefach from the ground and reaches up to ten Tefach from the ground, then some allow washing hands in that sink even initially.

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[1] Os Chaim 43:1; Kaf Hachaim 4:11; Y.D. 116:73; Minchas Yitzchak 4:37; Chelkas Yaakov 2:162; Yabia Omer 9:108; Piskeiy Teshuvos 4:19

Background: Although there is no prohibition in doing a Mitzvah within a bathroom [Darkei Teshuvah Yoreh Deah 19:21] nevertheless the question is raised whether the water in a bathroom is able to purify one’s hands. The Kaf Hachaim ibid differentiates between using the bathroom washing water for washing after use of the bathroom, which is permitted in a time of need, versus for washing in the morning after awakening, or for bread, in which case you say a blessing over it, and it is more stringent and the water is invalid. However, it is unclear if this invalidation is even with sink water or only with toilet water. See Devar Yehoshua 1:76; Piskeiy Teshuvos 160:19 footnote 73 who learns that it only applies to water that stayed in the bathroom for a while, and not to sink water

[2] Zechor Leavraham 3:49 and Zivcheiy Tzedek 2:116, brought in Kaf Hachaim 4:11 and 116:73, that so is the custom of the masses to spill out the water that they brought into the bathroom for washing purposes and they do not wash their hands with it even for the sake of washing hands after using the bathroom; Minchas Yitzchak 4:37

The reason: As a bathroom is a place of impurity and hence how can washing in it remove the impurity. [Minchas Yitzchak ibid in name of Poskim]

[3] Har Tzevi 1:50; Devar Yehoshua 1:76; Vayaan Yosef 1:2; Piskeiy Teshuvos 4:19; 160:19; 171:9

[4] Zechor Leavraham ibid; Os Chaim 43:1; Kaf Hachaim ibid; Piskeiy Teshuvos 4:19

[5] See Mishneh Halachos 5:2

[6] See Yabia Omer 3:1; Chazon Ish 24:26; Vayaan Dovid 1:1; Az Nidbaru 14:86; Piskeiy Teshuvos 4 footnote 192

[7] See Shem Mishimon O.C. 9; Kaf Hachaim 4:11; Y.D. 116:73; Os Chaim 43:1; Chazon Ish Netilas Yadayim 24:26; Eretz Tzefvi 1:110-111; Zekan Aaron 1:1; Chelkas Yaakov 1:2-4; 2:162; Minchas Yitzchak 1:60; 4:36; Divreiy Yisrael 1:8; Divrei Yatziv Y.D. 34; Devar Yehoshua 1:76; Yehsuas Moshe 1:31; 2:101; Or Letziyon 1:1; Kinyan torah 1:49; Vayaan Yosef 1:2; Yabia Omer 3:1-2; 9:108; Koveitz Mibeis Levi 7:71; Piskeiy Teshuvos 4:19; 160:19; 171:9

[8] Shem Mishimon O.C. 9; Os Chaim 43:1; Minchas Yitzchak 4:36; Chelkas Yaakov 2:162; Vayaan Yosef 1:2; Yabia Omer 9:108; Piskeiy Teshuvos 4:19; Kaf Hachaim 4:11; Y.D. 116:73 [The Kaf Hachaim ibid differentiates between using the bathroom washing water for washing after use of the bathroom, which is permitted in a time of need, versus for washing in the morning after awakening, or for bread, in which case you say a blessing over it and it is more stringent and the water is invalid. However, it is unclear if this invalidation is even with sink water or only with toilet water. See Devar Yehoshua 1:76; Piskeiy Teshuvos 160:19 footnote 73 who learns that it only applies to water that stayed in the bathroom for a while, and not to sink water]

Background: Although there is no prohibition in doing a Mitzvah within a bathroom [Darkei Teshuvah Yoreh Deah 19:21] nevertheless the question is raised whether the water in a bathroom is able to purify one’s hands as one who enters a bathroom [even without doing his needs] is impurified. Furthermore, perhaps the water in a bathroom is considered repulsive and is invalid for washing just as we rule regarding water that was drunk by a dog.

[9] The reason: 1) As one is not to perform a Mitzvah in an area that is forbidden to study Torah. [Shem Mishimon O.C. 9] As a bathroom is a place of impurity and hence how can washing in it remove the impurity. [Minchas Yitzchak ibid in name of Poskim]

[10] Os Chaim 43:1; Minchas Yitzchak 4:36; Piskeiy Teshuvos 4:19; 160:19 in name of all Poskim ibid

Other opinions: Some Poskim rule that one may not wash his hands for bread using water from a bathroom, being that the water is considered invalid. [Levushei Mordechai Tinyana 182; Possible implication of Ben Ish Chaiy Achreiy-Kedoshim 13 and Kaf Hachaim 4:11]

[11] See Yabia Omer 3:1; Chazon Ish 24:26; Vayaan Dovid 1:1; Az Nidbaru 14:86; Piskeiy Teshuvos 4 footnote 192

[12] Har Tzevi 1:50; Devar Yehoshua 1:76; Vayaan Yosef 1:2; Piskeiy Teshuvos 4:19; 160:19; 171:9

[13] Poskim ibid

[14] Ben Ish Chaiy Achreiy-Kedoshim 13; Kaf Hachaim 4:11 based on that this water is considered repulsive just like water which a pig drank from and which the Poskim rule is invalid [Admur 160:8; M”A 160:7; Bach 160, brought in Beir Heiytiv 160:8], and hence may not be used; Kaf Hachaim Y.D. 116:73; Daas Torah 160:4; Devar Yehoshua 1:76; See Piskeiy Teshuvos 160:19

Other opinions: Some Poskim rule that water from which a dog or pig drank from remains permitted to be used for washing hands for bread [Mamar Mordechai 160:6; 1^st and Stam opinion in Adcmur ibid; See Admur ibid who records opinion of Bach as Yeish Poslim] and the same would seemingly apply here regarding bathroom water. [See Kaf Hachaim 4:11]

[15] Devar Yehoshua 1:76; Piskeiy Teshuvos 160:19 footnote 73

[16] See Piskeiy Teshuvos 4:19; Chayeh Levi 1:14; Oar Letziyon 1:9