Measuring Instruments

Vernier Calliper

Determining Precision

Determining Precision

The precision (smallest possible measurement) can be determined using the following method: $\text{Precision}=\frac{\text{Value of 1 Main Scale Division}}{\text{Total Number of Vernier Scale Divisions}}$

Example

Example of a Main Scale and Vernier Scale

In this case:

• Value of 1 Main Scale Division: 1 mm
• Total Number of Vernier Scale Divisions: 20
• Precision: $\text{Precision}=\frac{1\text{ mm}}{20}=0.05\text{ mm}(0.005\text{ cm})$

Making a Measurement

Step 1: Main Scale Reading

The Main Scale Reading ($\mathrm{MSR}$) is the main scale division just before the zero (0) mark on the vernier scale

Main Scale Reading

In this case, the Main Scale Reading ($\mathrm{MSR}$) is $11\text{ mm}$.

Step 2: Vernier Scale Reading

1. Identify the line on the vernier scale that is exactly aligned with a division on the main scale.
2. Count on the vernier scale the number ($n$) of that line from the zero mark.
3. The vernier scale reading $\mathrm{VSR}$ is given by: $\mathrm{VSR}=\text{Precision}\times n$

Vernier Scale Reading

In this case, $n=13$ and $\text{Precision}=0.05\text{ mm}$: $\mathrm{VSR}=0.05\times 13=0.65\text{ mm}$

Step 3: Final Reading

The final reading is given by $\mathrm{MSR}+\mathrm{VSR}$ In this case, $11\text{ mm}+0.65\text{ mm}=11.65\text{ mm}$

Recording Measurements

Important

• Number of decimal places depends on the unit used to record the value.
• To find correct number of decimal places, convert the precision that was calculated in $\mathrm{mm}$ into the desired unit and count number of decimal places.

Example

If recording in millimetres ($\mathrm{mm}$): $0.05\text{ mm}÷1=0.05(\text{2 decimal places})$ If recording in centimetres ($\mathrm{cm}$): $0.05\text{ mm}÷10=0.005(\text{3 decimal places})$ If recording in metres ($\mathrm{m}$): $0.05\text{ mm}÷1000=0.00005(\text{5 decimal places})$