What is the formula for least count of a micrometer?

The least count of a micrometer refers to the smallest measurable value the instrument can detect. The formula used to calculate this value is both simple and powerful:

Least Count Formula for a Micrometer

Least Count (LC) = Pitch of the screw / Number of divisions on the circular scale

OR

Least Count (LC) = Number of divisions on the circular scale / Pitch of the screw

• Pitch: The distance the spindle moves forward (or backward) in one complete rotation of the thimble.
• Number of Divisions: Total number of graduations marked on the thimble or circular scale.

Understanding the Formula Step-by-Step

Let’s break it down:

• Pitch of the Screw
  Typically, a micrometer has a pitch of 0.5 mm — meaning the spindle advances 0.5 mm in one complete turn.
• Circular Scale Divisions (CSD)
  The rotating circular scale (thimble) usually has 50 or 100 divisions, depending on the model.

So if:

• Pitch = 0.5 mm
• CSD = 50 divisions

Then,

LC = 0.5 / 50 = 0.01 mm

That means the micrometer can measure up to 1/100^th of a millimeter.

Real-Life Example

Imagine you're working in a mechanical lab and want to know the smallest increment your micrometer can detect. You check the tool and find:

• Pitch: 0.5 mm
• Circular scale: 100 divisions

Using the formula:

LC = 0.5 mm / 100 = 0.005 mm

This is an ultra-precision micrometer with a least count of 5 microns!

Table of Common Configurations

Least Count vs Resolution vs Accuracy

• Least Count = Smallest measurable step
• Resolution = Ability to detect small changes (usually same as LC)
• Accuracy = Closeness to true value (depends on calibration, zero error, wear)

How to Remember the Formula

Think of the micrometer like a screw:

• Turning it moves a spindle.
• That movement is divided into small markings.
• The smaller the markings (i.e., the more divisions), the higher the precision.

That’s why the formula uses:
LC = movement in one rotation / number of steps (divisions)

Common Mistakes to Avoid

• Confusing pitch with least count: Pitch is the total movement per turn; LC is how finely it's broken up.
• Ignoring zero error before applying readings.
• Assuming all micrometers have the same LC — they don’t!