1. What is Relative Uncertainty?

Relative uncertainty (RU) is a measure of uncertainty relative to the size of the measurement result. It expresses the absolute uncertainty (AU) as a percentage of the measured value, providing a standardized way to compare uncertainties across different measurements.

2. How Does the Calculator Work?

The calculator uses the relative uncertainty formula:

Where:

• \( RU \) — Relative uncertainty (percentage)
• \( AU \) — Absolute uncertainty (same units as measurement)
• \( measured \) — Measured value (same units as AU)

Explanation: The formula converts the absolute uncertainty to a percentage of the measured value, allowing comparison between measurements of different magnitudes.

3. Importance of Relative Uncertainty

Details: Relative uncertainty is crucial in scientific measurements as it indicates the quality of the measurement. A smaller relative uncertainty means higher precision. It's particularly important when comparing measurements of different magnitudes.

4. Using the Calculator

Tips: Enter both absolute uncertainty and measured value in the same units. The measured value must be greater than zero. The result will be in percentage.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between absolute and relative uncertainty?
A: Absolute uncertainty has the same units as the measurement, while relative uncertainty is unitless (percentage) and shows uncertainty relative to the measurement size.

Q2: What are typical relative uncertainty values?
A: In most scientific work, relative uncertainties below 5% are generally acceptable, though requirements vary by field and application.

Q3: Can relative uncertainty be greater than 100%?
A: Yes, when the absolute uncertainty is larger than the measured value itself, though such measurements are usually considered unreliable.

Q4: How is relative uncertainty used in error propagation?
A: When combining measurements, relative uncertainties can be combined using specific rules depending on the mathematical operations involved.

Q5: Should I use relative or absolute uncertainty for reporting?
A: Both are often reported together - absolute uncertainty shows the actual uncertainty range, while relative uncertainty allows comparison between different measurements.