Percentage Error Calculator

Percentage Error Formula:

\[ \%E = \frac{(Q_{err} - X_E)}{X_E} \times 100\% \]

Percentage Error (\%E):

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1. What is Percentage Error?

Percentage Error is a measure of how inaccurate a measurement is, standardized to how large the measurement is. It quantifies the difference between an erroneous measurement and the true value as a percentage of the true value.

2. How Does the Calculator Work?

The calculator uses the Percentage Error formula:

\[ \%E = \frac{(Q_{err} - X_E)}{X_E} \times 100\% \]

Where:

\( \%E \) — Percentage Error
\( Q_{err} \) — Erroneous Quantity (measured or observed value)
\( X_E \) — True Value (expected or reference value)

Explanation: The formula calculates the relative error between the measured value and the true value, expressed as a percentage of the true value.

3. Importance of Percentage Error Calculation

Details: Percentage Error is crucial for assessing measurement accuracy in scientific experiments, quality control processes, and various engineering applications. It helps quantify the reliability of measurements and experimental results.

4. Using the Calculator

Tips: Enter the erroneous quantity (measured value) and the true value (expected value). Both values must be valid numbers, and the true value cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive percentage error indicate?
A: A positive percentage error indicates that the measured value is greater than the true value (overestimation).

Q2: What does a negative percentage error indicate?
A: A negative percentage error indicates that the measured value is less than the true value (underestimation).

Q3: What is considered an acceptable percentage error?
A: Acceptable percentage error varies by field and application. In many scientific contexts, errors below 5% are considered acceptable, but this depends on the specific requirements.

Q4: Can percentage error be greater than 100%?
A: Yes, percentage error can exceed 100% when the measured value is more than twice the true value.

Q5: How is percentage error different from absolute error?
A: Absolute error gives the actual difference between measured and true values, while percentage error expresses this difference relative to the true value as a percentage.