Calculate Relative Error

Relative Error Formula:

\[ \text{Relative Error} = \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \]

Relative Error:

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1. What is Relative Error?

Relative Error is a measure of the accuracy of a measurement compared to the true or accepted value. It expresses the magnitude of the error relative to the size of the true value, making it useful for comparing accuracy across different scales.

2. How Does the Calculator Work?

The calculator uses the Relative Error formula:

\[ \text{Relative Error} = \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \]

Where:

Measured Value — The value obtained from measurement
True Value — The known or accepted reference value

Explanation: The absolute difference between measured and true value is divided by the true value to give a dimensionless number, often expressed as a percentage.

3. Importance of Relative Error

Details: Relative error is crucial in scientific measurements as it allows comparison of measurement accuracy regardless of the scale of the values. It's particularly important in quality control, experimental physics, and engineering applications.

4. Using the Calculator

Tips: Enter both measured and true values in the same units. The true value cannot be zero (division by zero is undefined). The result is displayed as both a decimal and percentage.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between absolute and relative error?
A: Absolute error gives the magnitude of error in the same units as the measurement, while relative error shows the error relative to the size of the true value.

Q2: When is relative error more useful than absolute error?
A: Relative error is more useful when comparing measurements of different magnitudes or when the scale of measurement varies widely.

Q3: What is a good relative error value?
A: This depends on the field, but generally smaller is better. In many scientific applications, <5% is acceptable, while precision engineering might require <0.1%.

Q4: Can relative error be negative?
A: No, because the formula uses absolute value of the difference. It always represents the magnitude of error.

Q5: How is relative error related to percent error?
A: Percent error is simply relative error multiplied by 100 to express it as a percentage.