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Firstly:
A number of modern researchers have studied the weights, measures and lengths mentioned in the Qur’an and Sunnah. The scholars have discussed guidelines on their values in the past, and mentioned their equivalents in modern terms. These scholars include the following:
Secondly:
With regard to what the questioner wants to know about the modern equivalents of those measures, weights and volumes, we say – with the addition of the equivalent of the “meel”:
Shaykh ‘Abdullah ibn Sulaymaan al-Munayyi‘ (may Allah preserve him) said:
The mudd is equivalent to 544 grams, based on the fact that the mudd is equal to one and a third ratls, and the ratl is equivalent to 408 grams, as noted above.
Majallat al-Buhooth al-Islamiyyah (59/179).
Shaykh ‘Abdullah ibn Sulaymaan al-Munayyi‘ (may Allah preserve him) said:
The Council of Senior Scholars in the Kingdom of Saudi Arabia researched the equivalent of the saa‘ in kilograms, basing their research on the fact that the saa‘ of the Messenger of Allah (blessings and peace of Allah be upon him) was equal to four mudds, and the mudd was what could fill the cupped hands of a man of average size, then it was worked out what was meant by “what could fill the cupped hands of a man of average size”. The conclusion reached was that the mudd is equivalent to approximately 650 grams, so the equivalent of the saa‘ is 2600 grams.
Majallat al-Buhooth al-Islamiyyah (59/178).
Shaykh ‘Abdullah ibn Sulaymaan al-Munayyi‘ (may Allah preserve him) said:
The qullah that is well known among the scholars is the “qullah of Hajar”. This Hajar was a village near Madinah, not the Hajar of al-Bahrain.
We have mentioned above that one qullah was equal to two hundred and fifty ratls, and we have mentioned above that the ratl is equivalent to 408 grams. Therefore the equivalent of a single qullah in grams is 250 x 408 = 102,000 grams, or 102 kilograms.
Majallat al-Buhooth al-Islamiyyah (59/184).
Shaykh Wahbah az-Zuhayli (may Allah preserve him) said:
The dhiraa‘ [cubit] referred to in fiqh is the Haashimi dhiraa‘, which is equivalent to 61.2 centimetres.
The meel [mile] is 4,000 dhiraa‘s [cubits], i.e., 1,848 metres.
The farsakh [parasang] is 3 meels, or 5,544 metres, or 12,000 khutwah [steps].
The Arabian bareed is equal to 4 farsakhs, or 22,176 metres, or 22.176 kilometres.
Al-Fiqh al-Islami wa Adillatuhu (1/74, 75).
And Allah knows best.