The least count of a vernier bevel protractor

📌 Quick Answer

The least count of a universal vernier bevel protractor is 5 minutes of arc (5′), which is one-twelfth of a degree.

It comes from the vernier scale: 12 vernier divisions cover 23 degrees on the main scale, so one vernier division equals 1°55′, and the smallest angle the instrument can resolve is the 5′ difference between this and two main-scale degrees.

🔹 Key Takeaways

Least count = 5 minutes (5′) = 1/12 of a degree.
The main scale is graduated in whole degrees (0° to 360°).
The vernier has 12 divisions on each side of zero, spanning 23° of the main scale.
One vernier division = 23°/12 = 1°55′, and 2° minus 1°55′ = 5′, which is the least count.

What Is a Vernier Bevel Protractor?

A vernier bevel protractor is a precision angular measuring instrument used in machine shops and tool rooms to measure and mark angles to within a few minutes of arc. It is the most accurate of the simple protractors and is often called a universal bevel protractor because the adjustable blade and acute-angle attachment let it measure almost any angle from 0° to 360°.

It consists of a graduated circular dial (the main scale), a stock (base) that rests against one face of the work, an adjustable blade that touches the other face, and a vernier scale attached to the rotating dial that provides the fine reading.

Least Count and Its Derivation

The least count is the smallest angle the instrument can measure. For a standard universal bevel protractor it is 5 minutes (5′), derived as follows:

The main scale is divided into degrees, so one main-scale division = 1° = 60′.
The vernier scale carries 12 equal divisions on each side of its zero, and these 12 divisions occupy 23° on the main scale.
Therefore one vernier division = 23° ÷ 12 = 1°55′.
Least count = (2 main-scale divisions) − (1 vernier division) = 2°00′ − 1°55′ = 5′.

Expressed as a fraction of a degree, 5′ = 1/12° ≈ 0.0833°.

How to Take a Reading

Read the whole number of degrees on the main scale just before the vernier zero. Then find the vernier graduation that lines up exactly with a main-scale line and multiply its number by 5′. Add the two parts. For example, a main-scale reading of 34° with the 9th vernier line coinciding gives 34° + (9 × 5′) = 34°45′. Always note whether you are reading the vernier to the left or right of zero, because the bevel protractor reads in both directions.

Frequently Asked Questions

What is the least count of a vernier bevel protractor?

It is 5 minutes of arc (5′), which equals one-twelfth of a degree (about 0.0833°).

How is the least count of a bevel protractor calculated?

The main scale reads in degrees and the vernier has 12 divisions spanning 23°, so one vernier division is 1°55′. The difference between two degrees and one vernier division is 5′, which is the least count.

What is the range of a universal bevel protractor?

With its acute-angle attachment and reversible reading it can measure any angle from 0° to 360°.

Why is it called a universal bevel protractor?

Because the swivelling dial, sliding adjustable blade and acute-angle attachment let it measure a very wide range of angles, both acute and obtuse, on many shapes of work.