How to calculate the percentage uncertainty of a measurement?

To calculate the percentage uncertainty of a measurement, divide the uncertainty by the measured value and multiply by 100.

When making a measurement, there is always some degree of uncertainty due to limitations in the measuring device or the skill of the operator. To quantify this uncertainty, we can calculate the percentage uncertainty of the measurement. This is expressed as a percentage of the measured value, and tells us how much the measurement could vary from the true value.

To calculate the percentage uncertainty, we first need to determine the uncertainty in the measurement. This is typically given by the manufacturer of the measuring device, or can be estimated based on the precision of the device and the skill of the operator. Once we have the uncertainty, we divide it by the measured value and multiply by 100 to get the percentage uncertainty.

For example, if we measure a length of 10 cm with an uncertainty of 0.1 cm, the percentage uncertainty would be (0.1/10) x 100 = 1%. This means that the true value of the length could be anywhere from 9.9 cm to 10.1 cm, with a 68% confidence interval.

It is important to note that the percentage uncertainty is only an estimate of the true uncertainty, and does not take into account systematic errors or other sources of uncertainty. However, it is a useful tool for comparing the relative uncertainty of different measurements and determining the significance of any differences between them.