How To Convert Relative Uncertainty To Absolute Uncertainty

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.

Step 1

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.

Step 2

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.

Step 3

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

Step 4

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.