What is the difference between absolute uncertainty and relative uncertainty?

Conditions

• Applies to a measured quantity with a nonzero value when forming the relative ratio.
• The absolute uncertainty is expressed in the same units as the measured quantity.

Reasoning, step by step

1. Identify the measured quantity and its plus-or-minus amount.
2. Recognize that the plus-or-minus amount in the same units is the absolute uncertainty ($\delta x$).
3. Divide the absolute uncertainty by the measured quantity ($\frac{\delta x}{x}$).
4. Recognize that the resulting fraction or percentage is the relative uncertainty, which has no units.

Example

For a measured velocity of $13.2\,\text{m/s} \pm 0.2\,\text{m/s}$, the absolute uncertainty is $\delta v = 0.2\,\text{m/s}$. The relative uncertainty is $\frac{0.2\,\text{m/s}}{13.2\,\text{m/s}} = 0.0152 = 1.5\%$, which is unitless.

Common misconceptions

• Incorrectly attaching the original measurement units to the relative uncertainty.
• Confusing the absolute uncertainty symbol $\delta$ with the relative uncertainty ratio $\frac{\delta x}{x}$.
• Assuming relative uncertainty is always larger than absolute uncertainty.

Watch the explanation

Explore next

• Why is relative uncertainty computed as $\frac{\delta v}{v}$?
• How do you propagate uncertainty for products and quotients?
• What does the symbol $\delta$ mean in this lesson?