1. What is Percentage Error?

Percentage error is a measure of how inaccurate a measurement or calculation is, expressed as a percentage of the exact or true value. It quantifies the difference between an approximate value and the exact value relative to the exact value itself.

2. How Does the Calculator Work?

The calculator uses the percentage error formula:

Where:

• \( Approx \) — Approximate or measured value
• \( Exact \) — Exact or true value
• \( |Approx - Exact| \) — Absolute difference between values

Explanation: The formula calculates the absolute difference between approximate and exact values, divides by the exact value to get relative error, then multiplies by 100 to convert to percentage.

3. Importance of Percentage Error Calculation

Details: Percentage error is crucial in scientific experiments, engineering calculations, quality control, and data analysis to assess measurement accuracy and reliability. It helps identify systematic errors and evaluate the precision of experimental results.

4. Using the Calculator

Tips: Enter both approximate and exact values in the same units. The exact value cannot be zero (division by zero error). Values can be positive or negative, but the percentage error is always positive.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a good percentage error?
A: This depends on the field. In most scientific work, errors below 5% are generally acceptable, while in engineering, errors below 1% may be required.

Q2: Can percentage error be negative?
A: No, percentage error is always positive because it uses absolute value in the numerator. The direction of error (overestimate or underestimate) is indicated by the sign of (Approx - Exact).

Q3: What if the exact value is zero?
A: Percentage error cannot be calculated when the exact value is zero, as this would involve division by zero. In such cases, absolute error should be used instead.

Q4: How is percentage error different from percentage difference?
A: Percentage error compares a measured value to a known exact value, while percentage difference compares two experimental values where neither is considered "exact."

Q5: When should I use percentage error vs absolute error?
A: Use percentage error when you want to express the error relative to the size of the measurement. Use absolute error when the magnitude of error is more important than its relative size.