It was a little over 1/2 mile. As the comment above notes, the common cubit was about 18 inches, or 1.5 feet. Multiplied out, then 2,000 cubits comes to 3,000 feet, or 0.56 miles.
Excerpt from Barne's Notes on the Bible on Acts 1:12,
'A sabbath-day's journey - As far as might be lawfully traveled by a Jew on the Sabbath. This was 2,000 paces or cubits, or seven furlongs and a half - not quite one mile. See the notes On Matthew 24:20. The distance of a lawful journey on the Sabbath was not fixed by the laws of Moses, but the Jewish teachers had fixed it at 2,000 paces. This measure was determined on because it was a tradition that in the camp of the Israelites, when coming from Egypt, no part of the camp was more than 2000 paces from the tabernacle, and over this space, therefore, they were permitted to travel for worship. Perhaps, also, some countenance was given to this from the fact that this was the extent of the suburbs of the Levitical cities, Numbers 35:5. Mount Olivet was only 5 furlongs from Jerusalem, and Bethany was 15 furlongs. But on the eastern declivity of the mountain the tract of country was called, for a considerable space, the region of Bethany; and it was from this place that the Lord Jesus ascended." Source: here
And, an excerpt from Gill's Exposition:
"Which, is from Jerusalem a sabbath day's journey. The Syriac version renders it, "about seven furlongs", or near a mile; though Josephus (r) writes, that the Mount of Olives was but five furlongs from Jerusalem: perhaps this may be a mistake in the present copies of Josephus, since Chrysostom on this place cites this passage of Josephus, and reads seven furlongs; which exactly agrees with the Syriac version. A sabbath day's journey, according to the Jews, was two thousand cubits from any city or town, and which they often called, , "the bound of the sabbath" (s); and which they collect partly from Numbers 35:4 which they understand thus (t):
"a thousand cubits are the suburbs (of the city), and two thousand cubits the bounds of the sabbath. " Source is same as above.
The limitation of the travel allowed on the Sabbath was for travel outside of the city, and beyond the city gates. In Acts 1:12 the walk was from Jerusalem to the Mount of Olives.
Excerpt from Encyclopedia of the Bible:
"It is assumed that the regulation had its origin in the Mosaic period in the injunction to the Israelite not to leave camp to collect manna on the sabbath (Exod 16:29). In the Jerusalem Targ. this command reads: “Let no man go walking from the place beyond 2000 cubits on the seventh day.” There are other regulations to which appeal is made in an effort to locate the origin of this practice or precept. One is the provision that the area belonging to the Levitical cities included land which extended from the wall 2000 cubits on every side (Num 35:5). Another is the supposed distance that separated the Ark and the people both on the march and at camp (Josh 3:4). As far as this specific regulation is concerned, it applied only to leaving the city, the prescribed distance being measured from the city gate. Within the city proper, no matter how large it might be, there was no such limitation.
The original intent of the provision was to insure a quiet, leisurely Sabbath and to keep it from becoming a harried and busy day (Exod 16:29). It was also designed to keep the Israelitish worshiper in the area of the center of his worship. The motive was noble but, unfortunately, it resulted in a barren legalism. As a consequence, there were casuistic schemes to circumvent it. It did, however, permit a legitimate exception. If one were caught at a distance on a journey, he might travel to the nearest shelter for safety. But there were deliberate schemes to by-pass the rule. One such scheme was to select a tree or a stone at a distance, place some food there, and declare: “Let this be my residence.” ' Source: here
Stanley M. Horton, Th.d. has pointed out:
"Some later rabbis invented a tradition that enabled them to get around this limitation. For example, since they were allowed to go 1,000 yards from their home, they defined their home as anywhere their personal possessions were. They would take a bag of worthless possessions, go 1,000 yards, put down a personal possession, and say, "This is my Sabbath home; I can go another 1,000 yards." By this means, they could go anywhere they wanted. No wonder Jesus said, "You have let go of the commands of God and are holding on to the traditions of men" (Mark 7:8)." Source: here
This much the same information that Judaism teaches its followers today.
"Jewish law sets the maximum walking range from one’s city to 2,000 cubits (3,049.5 feet, 0.596 miles (960 meters). [However, this measurement starts 70 2/3 cubits (112.24 ft.) from the city limits.] Practically speaking, this means that you may not walk a straight line more than .598 miles (3161.74 ft.) in any direction in the wilds outside your city limits.
"City limits" are not defined by the map you carry in your glove compartment.
According to halachah, unless there is more than 70 2/3 cubits between one house and the next, all contiguous housing is considered to be part of the same city. Therefore at times it would be permitted to walk even from one city to the next, as long as the whole way is populated. This can be complex, and a rabbi should be consulted before planning a long trek on Shabbat." Source Chabad.org
The McLintock and Strong Biblical Cyclopedia offers:
"The Jewish scruple to go more than 2000 paces from his city on the Sabbath is referred to by Origen (περὶ ἀρχων, 4, 2), by Jerome (Ad Algasiam, qu. 10), and by Oecumenius — with some apparent difference between them as to the measurement. Jerome gives Akiba, Simeon, and Hillel as the authorities for the lawful distance. "
"Josephus (War, 5, 2, 3) makes the Mount of Olives to be about six stadia from Jerusalem; and it is the distance between these two places which in Ac 1; Ac 12 is given as a Sabbath day's journey. Josephus elsewhere determines the same distance as five stadia (Ant. 20, 8, 6); but both were probably loose statements rather than measured distances; and both are below the ordinary estimate of 2000 cubits. " Source: here
The entire entry at McLintock and Strong is of interest for the machinations the Jews invented to get around the limit on the Sabbath day.
See the Cubit Conversion Chart here. Bold emphasis is mine.