Short Answer:

The least count of a theodolite is the smallest angle it can measure accurately. It shows the precision level of the instrument. In simple terms, it tells how finely the theodolite can read and record angles.

For most vernier theodolites, the least count is 20 seconds, while for digital theodolites, it can be 5 seconds or even 1 second depending on the model. A smaller least count means the instrument is more precise and suitable for detailed and accurate surveying work.

Detailed Explanation:

Least count of a theodolite

The least count of a theodolite is defined as the smallest angle that can be read or measured using the instrument. It represents the precision of the theodolite and is very important in surveys where accuracy is required. The smaller the least count, the more precise the measurement will be.

In any angular measuring instrument, the least count is calculated using the values on the main scale and the vernier scale. For vernier theodolites, the least count is generally 20 seconds. This means the instrument can measure angles as fine as 20 seconds of a degree. Since 1 degree is divided into 60 minutes and each minute into 60 seconds, 20 seconds is a very small unit.

Formula for least count (in vernier theodolite):
Least count = (Value of one smallest division on main scale – Value of one division on vernier scale)
However, this formula is usually not required in digital instruments, as the least count is already displayed on the screen and handled internally.

Digital theodolites have better precision. Most digital models offer a least count of 5 seconds, 2 seconds, or even 1 second, making them ideal for highly precise tasks like tunnel construction, large bridges, and boundary marking. Because the readings are shown directly on the digital screen, chances of human error are very low.

Why is least count important?

• It helps in choosing the right theodolite for the job.
• For high-precision tasks like dam or highway construction, a lower least count (1 or 2 seconds) is required.
• For general field surveying, a 20-second least count is usually sufficient.
• It ensures accurate layout and angle setting during project work.

Example:
If the least count is 20 seconds and the instrument reads 30° 40′ 20″, then the surveyor knows the angle is accurate up to 20 seconds. If the actual angle is 30° 40′ 25″, this theodolite cannot detect that extra 5 seconds — it would round it off or miss it.

In practical surveying, using an instrument with a low least count helps in reducing total error and gives better results. The selection of theodolite based on least count depends on the required accuracy, type of work, and project budget.

Conclusion

The least count of a theodolite tells the smallest angle it can measure and directly affects the accuracy of surveying. Vernier theodolites usually have a least count of 20 seconds, while digital ones offer finer precision. Choosing the correct least count helps ensure reliable and precise angle measurements in civil engineering works.