How to Convert Relative Uncertainty to Absolute Uncertainty

How to Convert Relative Uncertainty to Absolute Uncertainty
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Uncertainty exists in laboratory measurements even when using the best equipment. For example, if you measure temperature using a thermometer with lines every ten degrees, you cannot be absolutely certain if the temperature is 75 or 76 degrees. Scientists report uncertainty as a range -- plus or minus -- around the reported value, such as 75 degrees Celsius, plus or minus 2 degrees Celsius. Uncertainty can be expressed as absolute -- in the units of the measurement -- or relative -- as a fraction of the measurement.

    Find the value of the relative uncertainty for the measurement. This is listed as a range after the measurement with no units, either as a decimal fraction or a percent. For example, given a measurement of 14.3 millimeters, plus or minus 5 percent, the relative uncertainty is 5 percent.

    Multiply the measurement by the relative uncertainty to obtain the absolute uncertainty. In this case, multiply 14.3 millimeters by 5 percent, which equals 0.7 millimeters.

    Write the measurement in terms of absolute uncertainty, in this case 14.3 millimeters, plus or minus 0.7 millimeters.

    Verify the results by dividing the absolute uncertainty by the measurement. For example, 0.7 millimeters divided by 14.3 millimeters equals 5 percent, which is the original relative uncertainty.


    • Absolute uncertainty is reported in the same units as the measurement.

      Relative uncertainty has no units associated with it.

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