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What Does Absolute and Relative Measurement Uncertainty Mean?

There are many reasons why measuring brings some measurement uncertainty: What you measure, the instrument you measure with, who is measuring and the surroundings in which you measure are some of them.

Theory

Absolute Uncertainty

Absolute uncertainty is the number that you need to add and subtract to find the accuracy range.

measurement \pm absolute uncertainty

Range of measurement (accuracy interval):

(lower boundary, upper boundary),

where

\begin{array}{l} lower boundary \\ = measurement - absolute uncertainty, \\ upper boundary \\ = measurement + absolute uncertainty . \end{array}

\begin{array}{l} lower boundary & = measurement - absolute uncertainty, \\ upper boundary & = measurement + absolute uncertainty . \end{array}

Formula

Relative Uncertainty

The relative uncertainty is a percentage, and the formula is as follows:

\begin{array}{l} relative uncertainty \\ = \frac{absolute uncertainty}{measurement} \cdot 100 % \end{array}

relative uncertainty = \frac{absolute uncertainty}{measurement} \cdot 100 %

Example 1

The weight of a stamp is estimated to be

1.10 \pm 0.02 g .

What is the interval for the measurement and what is the relative uncertainty?

The absolute uncertainty is $0.02$ . Therefore, the interval is

\begin{array}{l} lower boundary & = 1.10 - 0.02 = 1.08, \\ upper boundary & = 1.10 + 0.02 = 1.12 . \end{array}

This returns the measurement interval

(1.08, 1.12) .

That means the relative uncertainty is

\begin{array}{l} Relative uncertainty & = \frac{0.02 g}{1.10 g} = 0.0182 \\ = 1.82 % . \end{array}

Relative uncertainty = \frac{0.02 g}{1.10 g} = 0.0182 = 1.82 % .

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What Does Measurement Uncertainty Mean?

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