% Error Formula
What is % Error?
The percentage error, often written as % error or % difference, is used to describe the relative difference between a measured value and the true value of a quantity. It is a common way to express accuracy and precision in scientific and engineering measurements.
Calculating % Error
To calculate the percentage error, you use the following formula:
Where:
- % Error is the percentage error
- Measured Value is the value obtained from the measurement
- True Value is the known or accepted value of the quantity being measured
The absolute value (|) is used to ensure that the error is always positive. A positive % error indicates that the measured value is greater than the true value, while a negative % error indicates that the measured value is less than the true value.
Example of % Error Calculation
Suppose you measure the length of a rod and obtain a value of 10.2 cm. The true length of the rod is known to be 10.0 cm. The percentage error in this measurement is:
This indicates that the measured value is 2% greater than the true value.
Applications of % Error
Percentage error is used in a wide range of applications, including:
- Scientific measurements: To evaluate the accuracy of experimental results
- Engineering: To assess the precision of manufacturing processes
- Quality control: To monitor the consistency of products
- Data analysis: To compare different data sets
Reducing % Error
There are several techniques that can be used to reduce the percentage error in measurements:
- Using precise measuring instruments
- Calibrating measuring instruments regularly
- Taking multiple measurements and averaging the results
- Eliminating sources of error, such as environmental factors
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