Vernier calipers
Measures external cylinder diameters with 0.02 mm resolution using main scale and sliding vernier coincidence.
Physics / Vernier & micrometer metrology
FREE TO EXPLOREEXPERIMENT 14 · PHYSICS LABORATORY
Precision measurement of length, dimensions and determination of geometric scaling with Vernier calipers and micrometer gauges
Determine the fundamental circular geometric ratio π and investigate instrument zero errors and least count by precision measurement of cylinder diameters and circumferences using Vernier calipers and micrometer screw gauges. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
MEASURED CIRCUMFERENCE C—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
Simulation assumptions and limits
The simulation assumes an ideal Euclidean circular cylinder without surface ovality, taper, thermal expansion drift, or ribbon elasticity. Readings reflect standard metric least counts (caliper LC = 0.02 mm, micrometer LC = 0.01 mm, ribbon scale rounded to 0.02 mm) with true mathematical π = 3.14159265...
Know your apparatus.
Micrometer screw gauge
Calibrates small specimen diameters and sheet thickness with 0.01 mm resolution and friction ratchet.
Precision steel circumference ribbon rule
Wraps securely around the cylinder circumference to determine boundary perimeter C with anti-overlap vernier.
Set of calibrated cylindrical artifacts
Provides high-precision ground cylinders of diameters spanning 10.0 mm to 50.0 mm.
FOLLOW THE METHOD
A reason behind every step.
Determine the fundamental circular geometric ratio π and investigate instrument zero errors and least count by precision measurement of cylinder diameters and circumferences using Vernier calipers and micrometer screw gauges. Suggested independent settings: 15.0, 20.0, 25.0, 30.0, 35.0 mm.
Determine the least count and zero error of the calipers
Close the caliper jaws gently and observe whether the zero mark of the sliding vernier coincides with the zero mark of the main scale; record any positive or negative zero error.
Why this step matters
A persistent zero offset shifts every dimensional measurement by an additive constant, introducing systematic intercept error.
Inspect the micrometer screw gauge zero error
Clean the anvil and spindle faces with lens paper, rotate the ratchet thimble until it clicks three times against the anvil, and record any baseline circular division offset.
Why this step matters
Microscopic dust or grit on the anvil face causes a positive zero error that artificially enlarges all diameter readings.
Measure cylinder diameter at orthogonal orientations
Position the cylinder between the external caliper jaws perpendicular to the main beam, tighten the slide clamp gently, and read the main scale and matching vernier division.
Why this step matters
Measuring across two orthogonal axes and at multiple axial positions verifies that the cylinder is truly circular without ovality or taper.
Wrap the precision ribbon around the cylinder perimeter
Wrap the flexible steel ribbon snugly around the cylinder circumference without twisting or stretching, ensuring the ribbon edges align flat against the metal surface.
Why this step matters
Ribbon skew, tilt, or slack causes an overestimation of the circumference, distorting the geometric ratio.
Read circumference at the alignment index
Read the main scale on the ribbon and the coincidence index with a magnifying loupe to record the boundary circumference C to the nearest 0.02 mm.
Why this step matters
Parallax in reading flexible scale graduations introduces random reading scatter in the dependent variable.
Repeat for the complete series of diameters
Execute the diameter and circumference measurements for all five test cylinders spanning 15.0 mm to 35.0 mm to assemble the regression dataset.
Why this step matters
Evaluating multiple independent diameters across a wide dynamic range provides high statistical leverage for the slope determination.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
C = πd + b
| # | Cylinder diameter d (mm) | Measured circumference C (mm) | Diameter d (10⁻³ m) | Circumference C (10⁻³ m) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING