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Is it possible to convert between Torah measurements?

Specifically, T'fachim & Amot, (cubits) so I can figure out the size of the luchot (tablets) within the Aron Hakodesh (ark). (The Luchot are 6x6x3 t'fachim each [6 t'fachim cubed together] & the ark is 1.5 x 2.5x 1.5 cubits)

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You are asking 3 different questions. Please specify which is your primary intention: How many t'fachim are there in an ama? Can one convert between Biblical linear measurements (for not all t'fachim are biblical)? How much space did the luchos take up in the aron kodesh? Also see here on that last point. –  WAF Aug 3 '11 at 21:34
    
I edited to address your comments. –  zaq Aug 3 '11 at 21:57
    
4.5 according to wolframalpha. Though the gemara mentions 5 & 6. wolframalpha.com/input/?i=1+cubit+in+handbreadths –  Ariel K Aug 4 '11 at 2:57
    
wolframalpha.com/input/?i=1handbreadth+in+cubits it appears that hands and cubits are initially determined by inches, which means its not an ammah and a tefach. –  avi Aug 4 '11 at 7:53
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no error - each one is 6x6x3, (area = 108 t'fachim), there are two, so the total area is 216 t'fachim, or 6 cubed t'fachim when they are put together (216). –  zaq Aug 4 '11 at 13:51
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2 Answers

The gemara in Bava Batra 14a addresses the exact issue you seem to be inquiring about.

There is a Tanaic dispute as to how many tefachim are in a biblical amah:

  • R' Meir- 6 tefachim = 1 amah
  • R' Yehuda- 5 tefachim = 1 amah

The gemara then procceeds to evaluate the geometry involved with the Aron and its contents.

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There are two types of Amos: 5 tefach amos, 6 tefach amos. There are also "Sad" and "Happy" (if the tefach is with fingers stuck together or a bit loose) which are different by 1/2 finger.

Nowadays, calculating biblical sizes has such a wide margin of error (in addition to the "niskatnu habeitzim" debate), that most numbers that are given for tfachim/ammah are rounded lchumra. According to R' A"H Naeh, a tefach is 8cm.

http://hebrewbooks.org/shas.aspx?mesechta=3&daf=3b&format=text

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Which way is lechumra? –  Double AA Jan 25 '13 at 9:16
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