Percentage Uncertainty Calculator

Percentage Uncertainty Formula:

\[ \text{Percentage Uncertainty} = \left( \frac{\text{Uncertainty}}{\text{Value}} \right) \times 100 \]

Percentage Uncertainty:

1. What is Percentage Uncertainty?

Percentage uncertainty is a way to express the size of the uncertainty (error) in a measurement relative to the size of the measurement itself. It's commonly used in GCSE and A-Level science to compare the precision of different measurements.

2. How the Calculator Works

The calculator uses the percentage uncertainty formula:

\[ \text{Percentage Uncertainty} = \left( \frac{\text{Uncertainty}}{\text{Value}} \right) \times 100 \]

Where:

Uncertainty — The absolute uncertainty of your measurement (in the same units as the value)
Value — The measured value (must be greater than zero)

Example: If you measure a length as 12.5 cm with an uncertainty of 0.2 cm, the percentage uncertainty is (0.2/12.5) × 100 = 1.6%.

3. Importance in GCSE Science

Details: Percentage uncertainty helps students understand measurement precision, compare experimental results, and evaluate the reliability of data in their practical work and exams.

4. Using the Calculator

Tips:

Enter the absolute uncertainty (e.g., ±0.5 g → enter 0.5)
Enter the measured value
Both values must be positive, and the value cannot be zero
The calculator will give the percentage uncertainty to 2 decimal places

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between absolute and percentage uncertainty?
A: Absolute uncertainty has units (e.g., ±0.5 cm), while percentage uncertainty is unitless and shows the error relative to the measurement size.

Q2: How do I find the uncertainty of my measurement?
A: For digital instruments, it's typically ± the smallest division. For analog, it's often ± half the smallest division.

Q3: What's a good percentage uncertainty?
A: Lower is better. Under 5% is generally good for school experiments, but this depends on the specific investigation.

Q4: How is this used in combined calculations?
A: When combining measurements, percentage uncertainties are often added (for multiplication/division) or follow specific rules for other operations.

Q5: Why can't the value be zero?
A: Division by zero is mathematically undefined. In practice, measurements should never be exactly zero anyway.