How to Calculate Uncertainty

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Scientists account for the potential errors caused by equipment limitations or fluctuations in laboratory conditions by including an uncertainty value in their figures. This value is reported following a measurement or calculation to establish a range within which the true value might fall. Uncertainty can be calculated as an absolute value, or it can be calculated as a percentage or fraction of the true value.

Absolute Uncertainty

• Absolute uncertainty allows you to use a value expressed in the terms or units for which you are measuring. For example, if you are weighing an object on a scale with weight gradations one pound in size, the final weight you record may be incorrect by several ounces. To calculate the absolute uncertainty, take the smallest unit of instrument measurement and divide it in half. In the example of the scale, the smallest unit of measurement is one pound, so half of one pound, or 0.5 pounds, will represent your absolute uncertainty. You can then report the value for an object registering thirty pounds on this scale along with uncertainty as: 30 pounds +/- 0.5 pounds.

Relative Uncertainty

• You can also express the uncertainty in fraction or percentage form. This is called "relative uncertainty." To do so, you take your absolute uncertainty value and divide by the measurement or, using the previous example, 0.5 divided by 30, which results in a value of 0.017. You then report your value with this fractional uncertainty as: 30 pounds +/- 0.017 pounds. To record this value as a percentage uncertainty, you would multiple 0.017 by 100, resulting in a value written as: 30 lbs +/- 1.7 percent.

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