The Sages established rules for measuring the teĥum Shabbat as precisely as possible. First, they declared: “Teĥum Shabbat may be measured only with a rope that is fifty amot long, no more or less” (Eruvin 57b). If a longer rope were used, its weight would make it hard to pull taut, and the resulting measurement would be too short. If a shorter rope were used, one might pull it too tight, and the resulting measurement would be too long. Second, they required those measuring to hold the rope at chest height. If the person holding one end of the rope were to hold it at head level, while the person at the other end were to hold it at foot level, the resulting measurement would be too short (SA 399:1-3). Third, they said that when measuring an area that contains a valley, one person should stand on either side of the valley, so that they can measure the distance in the air. When measuring an area that contains a hill, tall poles should be set up so that the rope stretches above the hill. If the valley or hill is more than fifty amot wide, thus making it impossible to use a fifty-ama rope, the area should be measured with a four-ama rope. The person standing above should hold the rope at foot level, and the person standing below should hold it at chest level. If the slope is so steep that it would be difficult to calculate the measurement this way, the measurement should be estimated. If the area contains a cliff, as long as the cliff is less than four amot wide, it is not taken into account at all (Eruvin 58a-b; SA 399:4-5).
The Sages added that for these measurements, we rely only on an expert who knows how to calculate distances properly. If two experts arrive at different measurements, we follow the measurement that results in a larger teĥum. Since the laws of teĥum are rabbinic, we follow the more lenient opinion (Eruvin 58b-59a; SA 399:7-9). If one happens to spend Shabbat in a place where teĥum Shabbat has not been calculated, and he needs to go somewhere for the sake of a mitzva, he may take 2,000 medium-sized strides, which is approximately 2,000 amot (Eruvin 42a; SA 397:2; MB ad loc. 5).
Today it is best to establish teĥum Shabbat using aerial maps or GPS devices, as these can measure distances with extreme precision. We should not insist on measuring in the way that the Sages established. After all, their whole purpose was to measure as precisely as possible, using the tools available to them, without terribly inconveniencing those charged with measuring. Now that we have methods of measuring that are both more precise and more convenient, we must take advantage of them.