In a micrometer measurement experiment, the rotation of a screw is used to measure the thickness or diameter of a sample with high precision.
A typical outside micrometer combines readings from the sleeve main scale and thimble scale, allowing measurements to about 0.01 mm. Some models use a vernier scale or digital display to read even finer values.
For accurate measurement, it is important not to press the measuring faces strongly against the sample and to use the ratchet stop to apply a constant measuring force. The zero point must also be checked before measurement, and any offset must be corrected.
This article assumes an experiment in which the diameter of a metal wire or the thickness of a thin plate is repeatedly measured with an outside micrometer, and presents the introduction, precautions, result items, reference experimental values, calculations, sources of error, example result statement, and discussion examples.
Note:
This article is a study reference for discussing results obtained in physics experiments at schools, universities, and similar institutions. The experimental conditions and measured values shown here are illustrative examples, not actual measurement results.
Do not rotate the thimble while a finger is between the measuring faces. Excessive tightening can deform the sample or damage the instrument. Use the ratchet stop for final tightening so that measurements are made with a consistent force.
Dirt, oil, rust, or other contamination on the measuring faces can cause errors. Clean and store the instrument before and after use according to the laboratory manual or instructor’s directions.
- Basic Structure of a Micrometer
- How to Read the Scale
- Zero Correction
- Main Items to Record in the Results
- Reference Experimental Conditions
- Reference Experimental Values
- Calculation Methods
- Main Sources of Error
- Example of How to Write the Results
- Points to Connect the Results to the Discussion
- Discussion Example
- Summary
Basic Structure of a Micrometer
An outside micrometer consists of an anvil, spindle, sleeve, thimble, ratchet stop, clamp, and other components.
When the thimble is rotated once, the spindle moves a distance equal to the screw pitch. In a typical model, the screw pitch is 0.5 mm and the thimble is divided into 50 graduations.
Least count = screw pitch ÷ number of thimble divisions
= 0.5 mm ÷ 50
= 0.01 mm
How to Read the Scale
The measured value is obtained by adding the main-scale value shown on the sleeve to the thimble-scale value aligned with the reference line.
Measured value = sleeve reading + thimble reading
For example, if 5.5 mm is visible on the sleeve and the 28th thimble division aligns with the reference line, the measured value is 5.78 mm.
Zero Correction
If the instrument does not indicate 0.00 mm when the measuring faces are closed, the difference is called the zero error.
If the zero indication is e, the corrected value is calculated as follows.
Corrected value = reading − zero indication
For example, if the micrometer indicates +0.02 mm with the measuring faces closed, subtract 0.02 mm from each reading.
Main Items to Record in the Results
- Type of measuring instrument
- Micrometer measuring range
- Least count
- Instrument error or calibration information
- Zero indication
- Zero correction
- Object being measured
- Measurement position
- Measurement direction
- Reading for each trial
- Corrected measurement
- Number of measurements
- Mean
- Maximum and minimum values
- Range
- Standard deviation
- Standard error
- Relative standard deviation
- Temperature during measurement
- Any sample deformation or tilt noticed during measurement
Reference Experimental Conditions
| Item | Reference condition |
|---|---|
| Instrument | Outside micrometer |
| Measuring range | 0–25 mm |
| Scale division | 0.01 mm |
| Sample | Diameter of a metal wire |
| Zero indication | +0.02 mm |
| Number of measurements | 10 |
| Measuring force | Operate the ratchet stop about three times |
| Room temperature | 23 ℃ |
Reference Experimental Values
Metal Wire Diameter Measurement
| Trial | Reading (mm) | Zero correction (mm) | Corrected value (mm) |
|---|---|---|---|
| 1 | 1.26 | −0.02 | 1.24 |
| 2 | 1.27 | −0.02 | 1.25 |
| 3 | 1.26 | −0.02 | 1.24 |
| 4 | 1.25 | −0.02 | 1.23 |
| 5 | 1.27 | −0.02 | 1.25 |
| 6 | 1.26 | −0.02 | 1.24 |
| 7 | 1.28 | −0.02 | 1.26 |
| 8 | 1.25 | −0.02 | 1.23 |
| 9 | 1.26 | −0.02 | 1.24 |
| 10 | 1.27 | −0.02 | 1.25 |
Example of Thin-Plate Thickness Measurements at Different Positions
| Measurement position | Corrected thickness (mm) |
|---|---|
| Upper left | 0.82 |
| Upper right | 0.83 |
| Center | 0.82 |
| Lower left | 0.81 |
| Lower right | 0.83 |
Example of Measuring the Same Sample after 90-Degree Rotation
| Measurement direction | Diameter (mm) |
|---|---|
| 0° direction | 1.24 |
| 45° direction | 1.25 |
| 90° direction | 1.23 |
| 135° direction | 1.24 |
Calculation Methods
Reading the Scale
If the sleeve reads 7.5 mm and the thimble reads 23 divisions:
Thimble reading = 23 × 0.01
= 0.23 mm
Reading = 7.5 + 0.23
= 7.73 mm
Zero Correction
If the zero indication is +0.02 mm and the sample reading is 1.26 mm:
Corrected value = 1.26 − 0.02
= 1.24 mm
Mean
The mean of the ten corrected measurements is:
Mean = sum of measurements ÷ number of measurements
= 12.43 ÷ 10
= 1.243 mm
Maximum, Minimum, and Range
Maximum = 1.26 mm
Minimum = 1.23 mm
Range = maximum − minimum
= 1.26 − 1.23
= 0.03 mm
Standard Deviation
The sample standard deviation is calculated as follows.
s = √{Σ(xi − x̄)2/(n − 1)}
For the ten reference measurements, the standard deviation is approximately 0.0095 mm.
Standard Error
Standard error = s/√n
= 0.0095/√10
≈ 0.0030 mm
Relative Standard Deviation
Relative standard deviation (%) = s/x̄ × 100
= 0.0095/1.243 × 100
≈ 0.76%
Example of Reporting the Mean
When the measured value is reported together with the standard error:
Diameter = 1.243 ± 0.003 mm
If the laboratory manual specifies a method for expressing uncertainty, follow that method.
Area of a Circular Cross Section
If the measured wire diameter is 1.243 mm and the cross section is assumed circular:
A = π(d/2)2
= 3.14 × (1.243/2)2
≈ 1.21 mm2
Simple Evaluation of Roundness
If the maximum diameter measured in different directions is 1.25 mm and the minimum is 1.23 mm:
Diameter difference = maximum diameter − minimum diameter
= 1.25 − 1.23
= 0.02 mm
If this difference is sufficiently larger than the measurement error, the sample cross section may not be perfectly circular.
Main Sources of Error
| Source of error | Effect on measurement | Likely trend in results | Improvement |
|---|---|---|---|
| Zero error | Produces a constant offset in all measurements | All values become too high or too low | Check and correct the zero point before and after measurement |
| Dirty measuring faces | Adds the thickness of dirt or oil film | Values are larger than actual | Clean the measuring faces and sample |
| Different tightening force | Deforms the sample or instrument | Values vary by operator or trial | Use the ratchet stop |
| Excessive measuring force | Compresses soft samples | Values are smaller than actual | Use a small, consistent measuring force |
| Sample tilt | Measuring faces do not contact in parallel | Diameter or thickness tends to be overestimated | Position the sample correctly relative to the measuring axis |
| Different measurement positions | Captures nonuniform sample thickness or diameter | Measurements vary | Record positions and measure multiple locations |
| Noncircular sample cross section | Diameter differs with direction | Measurements change when the sample is rotated | Measure in multiple directions |
| Scale-reading error | Causes errors of 0.5 mm or 0.01 mm | Only some values deviate greatly | Check the main scale and thimble in sequence |
| Parallax | Misjudges alignment of the reference line and scale | Readings vary | View the scale straight on |
| Temperature change | Causes thermal expansion of the sample and instrument | Values change relative to the reference temperature | Allow them to equilibrate to room temperature |
| Heat from the hand | Warms the frame or sample | Values gradually change during repeated measurements | Hold the insulated section and avoid prolonged gripping |
| Spindle backlash | Position depends on rotation direction | Reading differs depending on approach direction | Approach the sample from the same direction |
| Wear of measuring faces | Reduces parallelism or flatness | Values vary by position | Inspect and calibrate regularly |
| Least-count limitation | Values below 0.01 mm cannot be read directly | Values occur in fixed increments | Use a higher-resolution instrument when necessary |
| Too few measurements | Random error cannot be evaluated adequately | Mean is less reliable | Take repeated measurements and perform statistical analysis |
Why Use the Ratchet Stop?
If the thimble is tightened directly by hand, the measuring force varies between operators. The ratchet stop helps hold the sample with nearly constant force and reduces variation caused by measuring force.
Why Measure Multiple Times?
Small random errors arise from scale reading, sample placement, tightening force, and other factors. Repeated measurements and averaging can reduce their influence.
However, systematic errors such as zero error cannot be removed simply by increasing the number of measurements and therefore require separate correction.
Why Change the Measurement Position?
The thickness of a thin plate or the diameter of a metal wire may not be perfectly uniform from place to place. Measuring multiple locations allows the sample’s own nonuniformity to be evaluated.
Why Change the Measurement Direction?
If the cross section of a metal wire is not perfectly circular, the measured diameter differs by direction. Rotating the sample during measurement can reveal flattening or deviation from circularity.
Example of How to Write the Results
The diameter of a metal wire was measured ten times using an outside micrometer with a least count of 0.01 mm.
The zero indication before measurement was +0.02 mm, so 0.02 mm was subtracted from each reading as a correction.
The corrected diameters ranged from 1.23 to 1.26 mm, with a mean of 1.243 mm, a standard deviation of 0.0095 mm, and a standard error of 0.0030 mm.
When the sample was rotated and measured, the maximum difference in diameter between directions was 0.02 mm.
Points to Connect the Results to the Discussion
- How large was the zero error?
- Was the sign of the zero correction correct?
- Was the variation in repeated measurements large compared with the least count?
- How large was the difference between the mean and individual measurements?
- Was the ratchet stop used consistently each time?
- Were the measuring faces and sample free of contamination?
- Was the sample held without tilting?
- Were there differences among measurement positions?
- Were there directional differences in diameter?
- Could the sample have been deformed or compressed?
- Was the temperature effect negligible?
- Were the significant figures appropriate for the instrument resolution?
Discussion Example
In this experiment, the diameter of a metal wire was repeatedly measured with an outside micrometer, followed by zero correction and statistical analysis.
When the measuring faces were closed before measurement, the micrometer indicated +0.02 mm. Because this condition makes dimensions appear 0.02 mm larger than their actual values, 0.02 mm was subtracted from every reading.
The ten corrected measurements ranged from 1.23 to 1.26 mm, with a mean of 1.243 mm and a standard deviation of 0.0095 mm.
Because the standard deviation was approximately equal to the micrometer’s least count of 0.01 mm, the variation was likely caused mainly by the scale-reading limit, slight differences in sample placement, and small differences in measuring force.
With a micrometer, tightening the thimble strongly by hand makes the measuring force inconsistent. Using the ratchet stop for final tightening likely reduced variation caused by measuring force to some extent.
Nevertheless, the observed range of 0.03 mm may have resulted from a metal-wire cross section that was not perfectly circular, slight differences in measurement position, or tilting of the sample relative to the measuring axis.
When the sample was rotated, diameters of 1.23–1.25 mm were obtained depending on direction. Because this difference exceeds the least count, it may reflect a slightly flattened cross section rather than scale-reading error alone.
Sample tilt can also produce a value larger than the actual diameter because the instrument then measures an oblique distance rather than the shortest distance.
Zero error is a systematic error and cannot be eliminated merely by repeating measurements and averaging them. The zero point must therefore be checked before measurement and the same correction applied to all measurements.
In contrast, variation caused by scale reading and sample placement is random error, whose influence can be reduced by increasing the number of measurements and calculating the mean.
Temperature can also cause error. Metal samples and micrometers expand with temperature, so prolonged handling or immediate measurement after bringing them from an environment at a different temperature may change their dimensions.
When measuring soft samples, excessive measuring force can compress them and produce values smaller than the true dimensions. This effect is relatively small for metal wire but requires particular attention for paper, resin, rubber, and similar materials.
Measurement accuracy can be improved by cleaning the measuring faces and sample, checking the zero point before and after measurement, using the ratchet stop, repeatedly measuring the same position, and additionally measuring at different positions and directions.
When reporting results, it is also important not to give unnecessarily many decimal places, considering that the instrument’s least count is 0.01 mm.
These results show that a micrometer can measure the diameter of a metal wire in increments of 0.01 mm and that zero correction, consistent measuring force, repeated measurements, and standardized measurement position and direction are necessary for reliable dimensional measurement.
Discussion Example When the Measured Value Was Larger Than the Reference Value
Possible reasons for a measured value larger than the reference value include failure to correct a positive zero error, dirt or oil film on the measuring faces, a tilted sample, or measurement along a direction with a larger diameter.
Discussion Example When the Measured Value Was Smaller Than the Reference Value
Possible reasons for a measured value smaller than the reference value include a negative zero error, compression of the sample by excessive tightening force, measurement along a direction with a smaller diameter, or a sample temperature below the reference temperature.
Discussion Example When the Measurements Varied Widely
Possible reasons for large variation include inconsistent use of the ratchet stop, different sample positions or directions in each trial, sample tilt, or reading the scale obliquely.
Discussion Example When Thickness Differed by Measurement Position
Differences in thickness among measurement positions suggest that the sample thickness was not perfectly uniform. However, if the differences are comparable to the least count, scale-reading error and differences in measuring force should also be considered, not only sample nonuniformity.
Summary
A micrometer is an instrument that uses the small displacement produced by a screw to measure sample thickness or diameter with high precision.
The measured value is read by adding the sleeve main scale and thimble scale, and any zero offset is corrected.
For reliable results, it is important to keep the measuring force constant with the ratchet stop and to take measurements repeatedly, at multiple positions, and in multiple directions.
In the discussion, factors such as zero error, measuring force, sample tilt, contamination of the measuring faces, temperature, sample nonuniformity, and least count should be related to deviations and variation in the measured values.
