Physics Tutorial: Measurement Uncertainty

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Each instrument has an inherent amount of uncertainty in its measurement. Even the most precise measuring device cannot give the actual value because to do so would require an infinitely precise instrument. A measure of the precision of an instrument is given by its uncertainty. As a good rule of thumb, the uncertainty of a measuring device is 20% of the least count. Recall that the least count is the smallest subdivision given on the measuring device. The uncertainty of the measurement should be given with the actual measurement, for example, 41.64 ± 0.02cm.

Here are some typical uncertainties of various laboratory instruments:

• Meter stick: ± 0.02cm
• Vernier caliper: ± 0.01cm
• Triple-beam balance: ± 0.02g
• Graduated cylinder: 20% of the least count

Here's an example. The uncertainty of all measurements made with a meter stick whose smallest division (or least count) is one millimeter is 20% of 1mm or 0.02cm. Say you use that meter stick to measure a metal rod and find that the rod is between 10.2 cm and 10.3cm. You may think that the rod is closer to 10.2cm than it is to 10.3cm, so you make your best guess that the rod is 10.23cm in length. Since the uncertainty in the measurement is 0.02cm, you would report the length of the metal rod to be 10.23 ± 0.02cm (0.1023 ± 0.0002 m).

When a quantity is graphed, it is common for the uncertainty of that quantity to be represented by error bars. For more information about error bars, see our Excel tutorial on using error bars.

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If you have a question or comment, send an e-mail to Lab Coordinator: Jerry Hester

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