How To Calculate Percentage Error

Percentage Error Formula:

\[ \% Error = \frac{|Experimental - True|}{|True|} \times 100 \]

Percentage Error:

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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 is the absolute value of the difference between experimental and true values divided by the absolute true value, multiplied by 100%.

2. How Does the Calculator Work?

The calculator uses the percentage error formula:

\[ \% Error = \frac{|Experimental - True|}{|True|} \times 100 \]

Where:

\( Experimental \) — The measured or experimental value
\( True \) — The actual or accepted true value
\( | | \) — Absolute value (always positive)

Explanation: The formula calculates the relative error as a percentage of the true value, providing a standardized measure of accuracy.

3. Importance of Percentage Error Calculation

Details: Percentage error is crucial in scientific experiments, quality control, and data analysis to quantify the accuracy of measurements and compare results across different scales and units.

4. Using the Calculator

Tips: Enter both experimental and true values. The true value cannot be zero (division by zero error). Values can be positive or negative, but the percentage error will always be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a good percentage error value?
A: This depends on the field and context. In some scientific fields, <5% is considered good, while in others, <1% may be required.

Q2: Can percentage error be negative?
A: No, percentage error is always positive because it uses absolute values in the calculation.

Q3: What's the difference between percentage error and absolute error?
A: Absolute error is the simple difference between experimental and true values, while percentage error expresses this as a percentage of the true value.

Q4: Why use absolute values in the formula?
A: Absolute values ensure the error is always positive, focusing on the magnitude of error rather than direction (overestimation vs underestimation).

Q5: What if the true value is zero?
A: Percentage error cannot be calculated when the true value is zero because it would involve division by zero. In such cases, absolute error should be used instead.