The vernier scale is one rechnological device that raises the sensitivity of one scale when its division is subdivided.

On this simulator the scale is 1:100, that means that the graved numbers are tenth hundredth part of the meter or the centimeter - bigger marks, that were subdivided by ten - smaller marks, the millimeter. The vernier has ten spaces between the vertical spaces, so, the instrument divides by ten the millimeter, the smaller division of the main scale, obtaining the tenth of millimeter 0.1mm.

In the metrology at metal mechanich section, this principle is used in many measurement instruments: caliper; micrometer and goniometer.

If you wish to know the mechanic of the utilization of the vernier in inch, interact with the simulators:

simulator of reading and interpretation of vernier in fractional inch and resolution 1/128"

simulator of reading and interpretation of vernier in thousandth inch and resolution 0.001"

To obtain more resolutions in millimeter:

reading and interpretation of vernier with main scale in millimeter abd resolution five hundredths of millimeter 0.05mm

reading and interpretation of vernier with main scale in millimeter and resolution two hundredths of millimeter 0.02mm

figure 1

measure with one scale with no vernier -
we only can infer the small value of the scale division

In the simulator in the end of the page, the vernier is the infeior scale, that slides under a main scale (scale 1:100 of meter - this means that the numbers of main scale express is centimeters, however, how this linear dimension is divided by nine strokes -ten spaces- the smallest division of the main scale is the millimeter).

The mark of the vernier that aligns with the races of teh main scale will provide the tenth measure, that has to be summed the the integer measure of the main scale (number of interval between the marks and teh zero (0) of the vernier in the left side).

Observe that when the zero of the vernier it is not perfectly aligned with some mark of the main scale we are not sure of its position (example.: __ 2 † 3 __ = 2.?) -in the given example, we can say that the value in the point '†' is bigger than 2.0 and smaller than 3.0. We just can assume one approximation more accurate: 2,4?; 2,5?; 2,6?;2,7? -figure 1.

figure 2

Sensitivity increasement of teh scale by addition of new marks - not legible

One possible solution would be dividing the spaces in the main scale, so that would have more marks, increasing the chace of the zero of the vernier align with some of them (example.: __ 2 ¡ ¡ ¡ ¡ ¡ † ¡ ¡ ¡ 3 __ = 2.6). However, this solution is restricted to human being vision limitations, among others -figur2 2.

Technically, what the vernier does is to increase the sensitivity of the main scale, when subdivining your smaller division - figure 3.

figure 3

formula to calculate the resolution of one instrument

By definition **resolution is teh smaller difference between indicators of one display device that can be significantly perceived **. This way, the smaller measure offered by one instrument is called 'resolution'. We can determin the resolution of the instrument dividing teh smaller division of the fixed scale by the number of divisions of teh vernier.

figure 4

measure with one scale provided of vernier -Increased sensitivity

On this simulator teh smaller division of the main scale - fixed scale - is one millimeter, that was divided by ten divisions of the vernier.

Resolution = 1mm / 10 = 0.1mm

The resolution of this simulator is one tenth of millimeter 0.1mm

## vernier scale in millimeter tenth resolution 0.1mm | reading | observation interpretation | ||
---|---|---|---|---|

scale | vernier scale | |||

1cm = 10mm + mm | 10 divisions 0.1mm | line gauge + vernier scale | ||

0 * 10mm + 0 * 1mm = 0mm | 3 * 0.1mm | 0mm + 0.3mm = 0.3mm | The zero of the vernier didn't get to the 1st big mark of the scale and get to the small one. In the vernier the 3rd mark is aligned Reading: 0.3mm | |

0 * 10mm + 2 * 1mm = 2mm | 5 * 0.1mm | 2mm + 0.5mm = 2.5mm | The zero of the vernier didn't get to the 1st big mark of the scale and passed to the 2nd small mark. In the vernier the 5th mark is aligned Reading: 2.5mm | |

1 * 10mm + 1 * 1mm = 11mm | 7 * 0.1mm | 11mm + 0.7mm = 11.7mm | The zero of the vernier passed of the 1st big mark of the scale and passed of the small 1st mark. In the vernier the 7th mark is aligned Reading: 11.7mm | |

3 * 10mm + 2 * 1mm = 32mm | 9 * 0.1mm | 32mm + 0,9mm = 32.9mm | The zero of teh vernier passed of the 3rd big mark of teh scale and passed of the small 2nd one. In teh vernier teh 9th mark is akigned.
Observe that the zero of the vernier almost get in the 3rd smallmark of the scale, and with no care, we could had read wrongly 33.9mm Reading: 32.9mm | |

4 * 10mm + 1 * 1mm = 41mm | 4.5 * 0.1mm | 41mm + 0.4 (5) mm = 41.4 (5) mm | The zero of the vernier passed of the 4th big mark of the scale and passed of the small 1st one. In the vernier the 4th mark passed a little bit, but didn't get in the 5th small one, so the interpretation is that is in the middle - 0.05mm Reading: 41.4(5)mm | |

The values between parenthesis (5) were obtained by interpolation | The resolution of the monitor can not allow that teh marks align theirselves perfectly, to solve that we added the small red circle |

See other examples of exercises commented vernier in tenths of a millimeter

- millimeter with tenth resolution (0.1mm)

- Virtual vernier scale - simulator of use and reading, resolution five hundredths of millimeter 0.05mm
- Virtual vernier scale - simulator of use and reading, resolution two hundredths of millimeter 0.02mm