Tosefet Shabbat

(לב) שַׁבַּ֨ת שַׁבָּת֥וֹן הוּא֙ לָכֶ֔ם וְעִנִּיתֶ֖ם אֶת־נַפְשֹׁתֵיכֶ֑ם בְּתִשְׁעָ֤ה לַחֹ֙דֶשׁ֙ בָּעֶ֔רֶב מֵעֶ֣רֶב עַד־עֶ֔רֶב תִּשְׁבְּת֖וּ שַׁבַּתְּכֶֽם׃ (פ)

Leviticus 23:32

(32) It shall be a sabbath of complete rest for you, and you shall practice self-denial; on the ninth day of the month at evening, from evening to evening, you shall observe this your sabbath.

ויקרא כ״ג:כ״ז

(כז) אַ֡ךְ בֶּעָשׂ֣וֹר לַחֹדֶשׁ֩ הַשְּׁבִיעִ֨י הַזֶּ֜ה י֧וֹם הַכִּפֻּרִ֣ים ה֗וּא מִֽקְרָא־קֹ֙דֶשׁ֙ יִהְיֶ֣ה לָכֶ֔ם וְעִנִּיתֶ֖ם אֶת־נַפְשֹׁתֵיכֶ֑ם וְהִקְרַבְתֶּ֥ם אִשֶּׁ֖ה לַיהוָֽה׃

Leviticus 23:27

(27) Mark, the tenth day of this seventh month is the Day of Atonement. It shall be a sacred occasion for you: you shall practice self-denial, and you shall bring an offering by fire to the LORD;

ויקרא כ״ג:כ״ח

(כח) וְכָל־מְלָאכָה֙ לֹ֣א תַעֲשׂ֔וּ בְּעֶ֖צֶם הַיּ֣וֹם הַזֶּ֑ה כִּ֣י י֤וֹם כִּפֻּרִים֙ ה֔וּא לְכַפֵּ֣ר עֲלֵיכֶ֔ם לִפְנֵ֖י יְהוָ֥ה אֱלֹהֵיכֶֽם׃

Leviticus 23:28

(28) you shall do no work throughout that day. For it is a Day of Atonement, on which expiation is made on your behalf before the LORD your God.

ראש השנה ט׳ א:ה׳-ז׳

ורבי ישמעאל מוסיפין מחול על קדש מנ"ל נפקא ליה מדתניא (ויקרא כג, לב) ועניתם את נפשותיכם בתשעה יכול בתשעה תלמוד לומר בערב אי בערב יכול משתחשך ת"ל בתשעה הא כיצד מתחיל ומתענה מבעוד יום מלמד שמוסיפין מחול על קדש אין לי אלא בכניסתו ביציאתו מנין ת"ל (ויקרא כג, לב) מערב עד ערב אין לי אלא יוה"כ שבתות מנין ת"ל תשבתו ימים טובים מנין ת"ל שבתכם הא כיצד כל מקום שיש בו שבות מוסיפין מחול על קדש

Rosh Hashanah 9a:5-7

The Gemara asks: If so, from where does Rabbi Yishmael derive this principle that one extends a sacred time period by adding from the profane to the sacred both before and after? The Gemara answers: He derives it from that which is taught in a baraita: The verse states, in reference to Yom Kippur: “And you shall afflict your souls on the ninth of the month in the evening” (Leviticus 23:32). One might have thought that one must begin to fast the entire day on the ninth of the month. Therefore, the verse states: “In the evening.” But if it is so that Yom Kippur begins in the evening, one might have thought that one need only begin to fast from when it is dark, after nightfall, when the tenth day of the month begins. Therefore, the verse states: “On the ninth.” How so; how is this to be accomplished? One begins to fast on the ninth of the month while it is still day. This teaches that one extends a sacred time period by adding at the beginning from the profane to the sacred. From here I have derived only that this addition is made at the beginning of Yom Kippur. But from where do I derive that a similar addition is made at the end of Yom Kippur? The verse states: “From evening to evening shall you rest on your Shabbat” (Leviticus 23:32), which teaches that just as Yom Kippur is extended at the beginning, so too, it is extended at the end. From here I have derived only that an extension is added to Yom Kippur. From where is it derived that one must also extend Shabbat? The verse states: “You shall rest [tishbetu],” which is referring to Yom Kippur but alludes to Shabbat. From where do I know that the same applies to Festivals? The verse states: “Your Shabbat [shabbatkhem],” your day of rest. How so? Wherever there is a mitzva of resting, be it Shabbat or a Festival, one adds from the profane to the sacred, extending the sacred time at both ends.

אורח חיים רס״א:ב׳

(ב) יש אומרי' שצריך להוסיף מחול על הקודש וזמן תוספת זה הוא מתחלת השקיע' שאין השמש נראת על הארץ עד זמן בין השמשות והזמן הזה שהוא ג' מילין ורביע רצה לעשותו כולו תוספת עושה רצה לעשות ממנו מקצת עושה ובלבד שיוסיף איזה זמן שיהיה ודאי יום מחול על הקודש ושיעור זמן בין השמשות הוא ג' רבעי מיל שהם מהלך אלף ות"ק אמות קודם הלילה: הגה ואם רוצה להקדים ולקבל עליו השבת מפלג המנחה ואילך הרשות בידו (טור ואגור בשם תוס' פ' תפלת השחר) [וע"ל סי' רס"ז]:

Shulchan Arukh, Orach Chayim 261:2

(2) 2. There are those who say that we must add from the weekday (mundane) to the holy and the time of this addition is from the beginning of sunset, i.e., when the sun is no longer visible on the earth’s [horizon], until bein hashmashos. This period is equivalent to the time [sufficient to walk] three-and-a-quarter mil (this is approx. 60 minutes). If one desires to deem this entire period of time as tosefes Shabbos (the addition to Shabbos), he may. If he wants to add less, he may. This is provided that one will add some amount of time when it is certainly day from the mundane to the holy. The time of bein hashemashos is 3/4 mil, which is like walking approximately 960 meters or .596 of a mile before nightfall. RAMA: And if one wishes to do this earlier and accepts Shabbos upon himself from Plag Hamincha and onward, he may do so. (Tur; Agur in the name of Tosefos)[See Siman 267].