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Percentage Uncertainty Formula:
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Percentage uncertainty (also called relative uncertainty) is a measure of the uncertainty of a measurement compared to the size of the measurement itself. It expresses uncertainty as a percentage of the measured value.
The calculator uses the percentage uncertainty formula:
Where:
Explanation: The formula shows what percentage the uncertainty is of the total measured value. A smaller percentage indicates more precise measurements.
Details: Percentage uncertainty is crucial in scientific experiments and measurements as it allows comparison of the precision of different measurements regardless of their scale. It helps determine the reliability of experimental results.
Tips: Enter both the uncertainty and value in the same units. The value must be greater than zero. The calculator will output the percentage uncertainty.
Q1: What's the difference between absolute and percentage uncertainty?
A: Absolute uncertainty has the same units as the measurement, while percentage uncertainty is dimensionless and allows comparison between different measurements.
Q2: What is a good percentage uncertainty?
A: This depends on the field, but generally under 5% is considered good for most applications, while under 1% is excellent.
Q3: How do I reduce percentage uncertainty?
A: Either reduce the absolute uncertainty (better instruments/methods) or increase the measured value (measure larger quantities).
Q4: Can percentage uncertainty be greater than 100%?
A: Yes, this occurs when the uncertainty is larger than the measured value itself, indicating very imprecise measurements.
Q5: How is this used in error propagation?
A: When combining measurements, percentage uncertainties can often be added in quadrature to find the total uncertainty.