מצות עשה לקום מפני כל חכם אפי' אינו זקן אלא יניק וחכים ואפי' אינו רבו (רק שהוא גדול ממנו וראוי ללמוד ממנו) (טור בשם הרמב"ם ור"ן פ"ק דקדושין) וכן מצוה לקום מפני שיבה דהיינו בן שבעים שנה (אפילו הוא ע"ה ובלבד שלא יהיה רשע) (ב"י בשם התוס' ובהגהות מיי' פ"ו ומרדכי פ"ק דקדושין ור' ירוחם ור"ן ור"ת):

Standing and showing honor before a sage, even if he is not one’s teacher. Containing 18 paragraphs: It is a positive commandment to stand up before any sage, even if he is not elderly but is a young scholar, and even if he is not one’s teacher (as long as he is greater than oneself and worthy of being learned from) (Tur quoting the Rambam and Ran, first chapter of Kiddushin). Likewise, it is a mitzvah to stand before an elderly person—i.e., someone aged seventy—even if he is an ignoramus, provided he is not wicked (Beit Yosef quoting Tosafot, Hagahot Maimoniyot ch. 6, Mordechai Kiddushin, Rabbeinu Yeruḥam, Ran, and Rabbeinu Tam).

From when is one obligated to stand before them? From the moment they enter within four cubits (about two meters) until they pass out of one’s line of sight. Someone riding is considered as walking.

It is forbidden to deliberately close one’s eyes before he reaches within four cubits in order to avoid having to stand up for him when he comes closer.

One does not stand for them in a bathroom or a bathhouse, as it is written: "You shall rise and show honor"—the standing must be accompanied by honor. (This refers specifically to the inner room of the bathhouse, but in the outer room one should stand.) (Beit Yosef quoting the Gemara, Rif, Rosh, Rabbeinu Yeruḥam, Aguda, and Sefer Mitzvot Gadol, negative commandment 22.)

Craftsmen are not obligated to stand before a Torah scholar while they are engaged in their work. If he is working for someone else and wants to be stringent with himself and stand, he is not permitted to do so.

A sage should not trouble the public by intentionally walking before them to cause them to stand. Rather, he should take a short route so as not to cause many people to rise; if he can avoid passing before them entirely, it is meritorious.

Even a scholar who is a youth must stand before an exceptionally elderly person. However, he is not obligated to rise to his full height, only enough to show honor. Even for an elderly non-Jew, one honors him with words and offers him a hand for support.

When two sages or two elderly men encounter one another, neither is required to stand for the other, but each should show some form of respect. (Even a teacher should show a bit of honor to his student) (from Hagahot Maimoniyot ch. 5 of Talmud Torah in the name of RaMaḥ).

One who sees a sage passing does not stand until the sage comes within four cubits, and once the sage passes in front of him, he may sit. If it is one’s primary teacher, one must stand when he is fully in view and remain standing until the teacher is hidden from view or sits in his place.

If someone is exceptionally wise—even if he is not one’s teacher—he is treated like a primary teacher. (Someone who is the greatest of the generation and publicly recognized as such is considered exceptionally wise) (Terumat HaDeshen §138 and Tosafot).

Even while one is studying Torah, one must stand before such a sage.

A sage, even if exceptionally wise, may choose to stand before someone who is known for outstanding deeds (Ran quoting the Ramban).

One who sees the head of the court (Av Beit Din) must stand when he sees him from a distance with full vision and remain standing until he passes within four cubits.

One who sees the Nasi (head of the Sanhedrin) must stand when he is fully in view and not sit until the Nasi either sits down or is no longer visible. All of them, if they waive their honor, it is waived. Nevertheless, it is still a mitzvah to honor them and stand before them to some extent.

When the Nasi enters the study hall, all stand and do not sit until he tells them to sit. When the head of the court enters, they form rows standing on each side until he sits in his place. When a sage enters, anyone within four cubits must stand; one person may be standing and one sitting until the sage reaches his place.

Sons of sages and Torah scholars, when the public needs them, may walk over the heads of the people (i.e., walk through the crowd) to reach their place. It is not praiseworthy for a Torah scholar to be the last to enter. If he left temporarily for his needs, he may return to his place.

Sons of sages whose fathers serve as leaders of the community, if they have the maturity to understand and listen, may sit before their father and turn their faces toward him. If they are not mature enough to understand, they should face the people.

If an outstanding young Chacham is with a very old moderate Chacham, regarding sitting in judgment or Torah, we seat the younger, greater Chacham at the head and he speaks first. At a drinking feast or wedding feast, we follow seniority and seat the oldest at the head. If the younger is an outstanding Chacham, and the elder is not so old, the Chacham always comes first. If the elder is exceedingly old, and the Chacham is not so outstanding, the elder always comes first, since he is somewhat Chacham. If neither is so Chacham or so old, the elder is first in every case.