1. What is Percentage Uncertainty?

Percentage uncertainty (PU) is a measure of the uncertainty of a measurement compared to the size of the measurement itself. It expresses the absolute uncertainty as a percentage of the measured value.

2. How Does the Calculator Work?

The calculator uses the percentage uncertainty formula:

Where:

• \( PU \) — Percentage uncertainty (%)
• \( uncertainty \) — Absolute uncertainty in the measurement
• \( value \) — The measured value

Explanation: The formula calculates what percentage the uncertainty is of the total measured value, providing a relative measure of error.

3. Importance of Percentage Uncertainty

Details: Percentage uncertainty is crucial in scientific measurements as it allows comparison of the precision of different measurements regardless of their scale. It's particularly important in physics, chemistry, and engineering experiments.

4. Using the Calculator

Tips: Enter both the absolute uncertainty and the measured value in the same units. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between absolute and percentage uncertainty?
A: Absolute uncertainty is the actual error margin (e.g., ±0.1 cm), while percentage uncertainty expresses this as a percentage of the measured value.

Q2: What are typical percentage uncertainty values?
A: In most scientific work, values under 5% are generally acceptable, though this depends on the specific application.

Q3: How do I determine the uncertainty value?
A: Uncertainty is often half of the smallest division on a measuring instrument, or it may be provided by the instrument's specifications.

Q4: Can percentage uncertainty be greater than 100%?
A: Yes, if the uncertainty is larger than the measured value itself, though this usually indicates very imprecise measurements.

Q5: How is percentage uncertainty used in calculations?
A: When combining measurements, percentage uncertainties can be added (for multiplication/division) or used to calculate propagated error.