shiurim measurements - How large was the menorah?

This question asking why the menorah didn't have rings and staves for carrying reminded me that, unlike with the other mishkan objects, we're not given any dimensions for the menorah. I've always imagined it as large enough to stand on the ground and provide overhead light. (That image is probably reinforced by the arch of Titus, but I'd be cautious about inferring too much from that.) But was it?

According to Rashi on Shemot 25:31, the menorah was cast from a talent of gold weighing 64 pounds (citing Tan. Beha’alothecha 3). The size question also came up in our torah study recently, where none of the chumashim on hand provided illumination. An engineer who was present told us that that amount of gold would yield something closer to a table lamp than a floor lamp. This site says that a kilo (2.2 pounds) of gold is about the size of an iPhone 6. 30 of those doesn't seem enough to make a large, solid (not hollow) menorah.

I know that the group in Jerusalem who are building utensils for the third temple interpret it as a floor lamp, like what I imagined. I don't know their sources.

How tall was the menorah? Sources, please.

Answer

The Talmud says on Menachot 28b:

אמר שמואל משמיה דסבא

גובהה של מנורה שמנה עשר טפחים

הרגלים והפרח ג' טפחים וטפחיים חלק וטפח שבו גביע וכפתור ופרח וטפחיים חלק וטפח כפתור ושני קנים יוצאין ממנו אחד אילך ואחד אילך ונמשכין ועולין כנגד גובהה של מנורה וטפח חלק וטפח כפתור ושני קנים יוצאין ממנו אחד אילך ואחד אילך נמשכין ועולין כנגד גובהה של מנורה וטפח חלק וטפח כפתור ושני קנים יוצאין ממנו אחד אילך ואחד אילך ונמשכין ועולין כנגד גובהה של מנורה וטפחיים חלק נשתיירו שם ג' טפחים שבהן ג' גביעין וכפתור ופרח

Samuel said in the name of an old scholar, The height of the candlestick was eighteen handbreadths: three handbreadths for the base and the flower upon it, two handbreadths plain, one handbreadth for cup, knop and flower, again two handbreadths plain, one handbreadth for a knop out of which two branches come forth, one on each side, extending and rising to the same height as the candlestick, then one handbreadth plain, one handbreadth for a knop out of which two branches come forth, one on each side, extending and rising to the same height as the candlestick, then again one handbreadth plain, and one handbreadth for a knop out of which two branches come forth, one on each side, extending and rising to the same height as the candlestick, and then two handbreadths plain; there now remained three handbreadths, in which space were three cups, a knop and a flower.

^{Translation from Soncino, via halakhah.com PDF.}

Assuming the value in this OU glossary of 3.2 inches per tefach, that comes to about 58 inches tall.