Short answer: Divide the absolute uncertainty by the absolute value of the result. To express relative uncertainty as a percentage, multiply by 100. To express relative uncertainty as a part per million, multiply by 1,000,000.
Step-by-Step Instructions: Relative Uncertainty as a Percentage
- Calculate the absolute expanded uncertainty.
- Divide the absolute uncertainty by the absolute value of the result.
- Multiply the result by 100.
- Report the relative uncertainty with a % symbol.
Step-by-Step Instructions: Relative Uncertainty as a Part per Million
- Calculate the absolute expanded uncertainty.
- Divide the absolute uncertainty by the absolute value of the result.
- Multiply the result by 1,000,000.
- Report the result with one of the following units of measurement:
- Parts in 106
- µUnit/Unit
Example
Here are some common examples of relative uncertainty.
Example 1: Lead (Pb) concentration of a sample using ICP-MS
10.00 ± 0.87 µg/L
(0.87 µg/L / 10.00 µg/L) x 100 = 8.7 %
Example 2: Length measured with a universal measuring machine
100.000000 ± 0.000051 mm ± 0.51 µm/m
(0.000051 mm / 100.000000 mm) x 1,000,000 = 0.51 µm/m
Example 3: Voltage measured with an 8.5-digit digital multimeter
10.00000 ± 0.00047 V
(0.00047 V / 10.00000 V) x 1,000,000 = 4.7 µV/V
Relative Uncertainty Calculator
Click the link below to download the relative uncertainty calculator
Download: ISOBudgets Relative Uncertainty Calculator – Version 1.0
FAQ
What is relative uncertainty?
Relative uncertainty is measurement uncertainty divided by the absolute value of the measurement or result so it can expressed in a term relative to the measurand, such as a percentage, parts-per-million, etc.
What is the difference between relative and absolute uncertainty?
Relative uncertainty is expressed in a term relative to the measurand (e.g. percent, part-per-million, etc) while absolute uncertainty is expressed in the same unit of measurement as the measurand.
How to calculate RSD in chemistry?
In chemistry, RSD is typically expressed as a percentage. To calculate it, first calculate the standard deviation. Next, divide the standard deviation by the absolute value of the result (typically, a concentration). Multiply the result by 100 to get RSD as a percentage.
If RSD needs to be expressed as an expanded uncertainty, determine the desired level of confidence (Typically, 95.45 %). Next, calculate the degrees of freedom and use the t-distribution to find the coverage factor. Then, multiple the percent RSD by the coverage factor.
What is the difference between relative uncertainty and relative standard deviation?
Relative standard uncertainty and relative standard deviation have similar confidence intervals. Both represent a standard deviation with a 68.27 % confidence interval. If either one is to be expressed as an expanded uncertainty (i.e. JCGM 100:2008, ISO 21748, or ISO 19036), they need to be multiplied by a coverage factor that produces a desired level of confidence.
However, relative uncertainty and relative standard deviation can have different confidence intervals. For example, a relative uncertainty can represent an expanded uncertainty with a 95.45 % confidence interval while a relative standard deviation represents a standard deviation with a 68.27 % confidence interval.
What is the difference between relative and absolute accuracy?
According to Fluke and Transmille equipment specifications, absolute accuracy contains all sources of error including the uncertainty of the calibration reference standard while relative accuracy contains all sources of error except the uncertainty of the calibration reference standard. The absolute accuracy is recommended for use if the equipment is calibrated by the respective manufacturer’s calibration facilities while the relative accuracy should be used in combination with the reference standard uncertainty if the equipment is calibrated by a laboratory other than the manufacturer.
What is relative standard uncertainty?
Relative standard uncertainty is a standard deviation of standard uncertainty expressed in relative terms, such as percentage, part-per-million, or equivalent.
Glossary
- Measurement Uncertainty
- non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used. (Source: JCGM 200:2012, 2.26)
- Measurand
- quantity intended to be measured. (Source: JCGM 200:2012, 2.3)
- Relative Measurement Uncertainty
- measurement uncertainty expressed in a term relative to the measurand.
- Absolute Measurement Uncertainty
- measurement uncertainty expressed in the same unit of measurement as the measurand.
- CMC Uncertainty
- calibration and measurement capability uncertainty available to customers under normal conditions as described in a laboratory’s scope of accreditation or published in the BIPM key comparison database (KCDB). (Source: ILAC P14:09/2020)