What Is Absolute Uncertainty?
Absolute uncertainty expresses the range within which the true value of a measurement is expected to lie, in the same units as the measurement itself. For example, a length recorded as 12.5 cm with an absolute uncertainty of 0.3 cm means the true value is expected to fall between 12.2 cm and 12.8 cm.
Absolute uncertainty can be read directly from an instrument or derived from the relative uncertainty, which states the uncertainty as a fraction (or percentage) of the measured value. It is essential for reporting experimental results, comparing instruments, and combining errors in later calculations, because it tells you how much trust to place in a single measured number.
Formula
Δx = ε × |x|
ε = Δx / |x|
where:
Δx = absolute uncertainty
ε = relative uncertainty (as a fraction, e.g. 0.02 = 2%)
x = measured value
Applications
- Reporting measurement error in physics and chemistry laboratory work
- Setting tolerance ranges for manufactured or machined parts
- Converting a percentage accuracy specification into a concrete range
- Preparing uncertainty budgets for calibration and metrology
Sources
- BIPM JCGM 100:2008. Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM).
- Taylor, J. R. (1997). An Introduction to Error Analysis (2nd ed.). University Science Books.