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What Is a Vernier Scale?

By Paul Reed
Updated May 17, 2024
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A vernier scale is a series of measuring lines added to micrometers, calipers and weighing devices to improve measurement accuracy. It was created by French mathematician Pierre Vernier in 1631. The principle is to place a second scale next to the primary scale with a different spacing of the scale lines. This is typically ten lines or units for every nine of the primary scale. The human eye is quite adept at determining when lines fall adjacent to each other, which is how a vernier reading is obtained.

Any measurement that falls between the lines of the primary can be determined by where the vernier mark aligns with the main scale. For example, if a measurement indicated between 50 and 51, regardless of the units, the vernier will align with the main scale at a value between 51 and 60 on the main scale. The vernier scale will normally show lines of 0 to 10, so if the alignment occurs at 7 on the vernier scale, the measurement would be 50.7.

Micrometers and calipers used for precision machining need accuracy to very small values. These devices typically have a stationary arm and a movable arm to adjust for the shape of the object, with measuring scales along the movable arm. Accuracy to one-thousandth of an inch or millimeter is often required. Adjusting the vernier scale to read 20 increments for every 19 on the main scale can improve this accuracy further. Rotary dial vernier scales can add additional accuracy by taking advantage of the circumference of the dial circle, which adds additional precision.

Vernier scales can be flat scales, as are common on slide calipers to measure inside or outside dimensions of objects. Dial micrometers are commonly used to measure the outside dimensions of smaller objects, with the rotary dial scales offering higher precision. Laboratory balances used for precision weight measurement of laboratory samples may use a digital dial or slide dial with a vernier to provide greater accuracy.

Other devices also use a vernier scale for measurement accuracy. Sextants, used by mariners for celestial navigation, use vernier scales for measuring the angles of the sun or stars above the horizon. Slide rules, analog mechanical computers invented in the 1600s, use vernier scales for improving the accuracy of mathematical calculations. Slide rules were commonly used for construction, engineering and aerospace until electronic calculators and computers became affordable to the average consumer in the 1970s.

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