Science, Tech, Math › Science The Relative Uncertainty Formula and How to Calculate It Share Flipboard Email Print Rafe Swan/Getty Images Science Chemistry Chemical Laws Basics Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Anne Marie Helmenstine, Ph.D. Chemistry Expert Ph.D., Biomedical Sciences, University of Tennessee at Knoxville B.A., Physics and Mathematics, Hastings College Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. She has taught science courses at the high school, college, and graduate levels. our editorial process Facebook Facebook Twitter Twitter Anne Marie Helmenstine, Ph.D. Updated December 09, 2019 The relative uncertainty or relative error formula is used to calculate the uncertainty of a measurement compared to the size of the measurement. It is calculated as: relative uncertainty = absolute error / measured value If a measurement is taken with respect to a standard or known value, calculate relative uncertainty as follows: relative uncertainty = absolute error / known value Absolute error is the range of measurements in which the true value of a measurement likely lies. While absolute error carries the same units as the measurement, relative error has no units or else is expressed as a percent. Relative uncertainty is often represented using the lowercase Greek letter delta (δ). The importance of relative uncertainty is that it puts error in measurements into perspective. For example, an error of +/- 0.5 centimeters may be relatively large when measuring the length of your hand, but very small when measuring the size of a room. Examples of Relative Uncertainty Calculations Example 1 Three 1.0 gram weights are measured at 1.05 grams, 1.00 grams, and 0.95 grams. The absolute error is ± 0.05 grams.The relative error (δ) of your measurement is 0.05 g/1.00 g = 0.05, or 5%. Example 2 A chemist measured the time required for a chemical reaction and found the value to be 155 +/- 0.21 hours. The first step is to find the absolute uncertainty: absolute uncertainty = 0.21 hoursrelative uncertainty = Δt / t = 0.21 hours / 1.55 hours = 0.135 Example 3 The value 0.135 has too many significant digits, so it is shortened (rounded) to 0.14, which can be written as 14% (by multiplying the value times 100). The relative uncertainty (δ) in the measurement for the reaction time is: 1.55 hours +/- 14% Sources Golub, Gene, and Charles F. Van Loan. "Matrix Computations – Third Edition." Baltimore: The Johns Hopkins University Press, 1996.Helfrick, Albert D., and William David Cooper. "Modern Electronic Instrumentation and Measurement Techniques." Prentice Hall, 1989.