Screw gauge: least count and reading

How do you find the pitch?

The pitch is the distance the screw moves in one complete turn of the head. To find it, turn the screw through x complete rotations and read how far it has moved on the linear scale, y. Pitch = y ÷ x. NCERT’s Class 11 manual says the pitch is usually 1 mm or 0.5 mm.

Least count of a screw gauge

One division of the circular scale moves the screw by pitch ÷ n, where n is the number of circular scale divisions. That is the least count.

NCERT notes that gauges with a least count of 0.001 mm are called micrometer screws. In workshops the same instrument is the outside micrometer.

How do you read a screw gauge?

1. Linear scale reading: the last mark on the linear scale visible at the edge of the circular scale. On a 0.5 mm gauge, check whether a half-millimetre line is showing.
2. Circular scale reading: the division that lies on the reference line of the linear scale.
3. Reading = linear scale reading + circular scale division × least count.
4. Subtract the zero error with its sign.

NCERT’s example: linear scale 0.5 cm, circular scale 2, least count 0.001 cm: 0.5 + 2 × 0.001 = 0.502 cm.

• 0.5 mm pitch, 50 divisions: linear scale shows 3.5 mm, circular scale 27 → 3.5 + 27 × 0.01 = 3.77 mm.
• 1 mm pitch, 100 divisions: linear scale shows 2 mm, circular scale 46 → 2 + 46 × 0.01 = 2.46 mm.

Positive and negative zero error

Bring the screw onto the stud with the ratchet. If the circular scale zero is on the reference line, there is no zero error. If the reading is more than zero, the zero error is positive; if less than zero, negative.

• Positive: the closed gauge reads a small number n just above zero: zero error = +n × LC. Division 2 on a 0.01 mm gauge gives +0.02 mm.
• Negative: the closed gauge reads just below zero, so the reference line shows a high division n of N: zero error = −(N − n) × LC. Division 97 on a 100-division gauge gives −(100 − 97) × 0.01 = −0.03 mm.

Correct every reading: true reading = observed reading − zero error. With +0.02 mm, 3.77 mm becomes 3.75 mm; with −0.03 mm, 2.46 mm becomes 2.49 mm.

The ratchet and backlash error

Turn the screw onto the object with the ratchet and stop at the first click. Turning the head itself can press too hard and change a thin wire’s diameter. NCERT asks for readings at no fewer than four points along a wire, each taken this way.

Backlash error comes from play between worn threads of the screw and the nut: the screw can slip a short distance without turning. NCERT’s advice is to move the screw in one direction only while taking readings. It can be reduced this way but not removed completely.

Measuring the diameter of a wire (Class 11 practical)

A wire may not be round or uniform. In NCERT Experiment 2, measure the diameter d₁ at one place, turn the wire through 90° at the same cross-section and measure d₂, take d = (d₁ + d₂)/2, and repeat at three more places along the wire. Average the values, then subtract the zero error.

A rough check with a metre scale catches a reading that is off by a factor of 10 or 100, which usually comes from a slip in the units.

Do you estimate the last digit?

It depends on the course. NCERT treats the least count, 0.01 mm, as the smallest length the gauge measures. Some Chinese physics lab handouts ask for one estimated digit, to 0.001 mm; with that rule, a line sitting exactly on division 27 is written 3.770 mm. Follow your handout or teacher.

Practising in KELIBRON

The lab’s mechanical outside micrometer is a 0–25 mm screw gauge with a 0.5 mm pitch and 50 thimble divisions, so its least count is 0.01 mm; its digital version reads to 0.001 mm. Practise reading on the Ø12 pin, and the thickness of a 0.50 mm steel shim, like the sheet in the NCERT practical. The “Zero not set” wrong use adds +0.02 mm to the reading. The lab has no 1 mm pitch, 100-division gauge and does not simulate backlash.