Relative static error, also known as relative error or relative uncertainty, is a concept used in measurement and instrumentation to quantify the accuracy or precision of a measurement compared to the true value or a reference standard. It's a way to express the magnitude of the measurement error as a percentage or a fraction of the true value.
Mathematically, the relative static error is calculated using the following formula:
Relative Error (%) = (|Measured Value - True Value| / True Value) * 100%
Where:
Measured Value: The value obtained from the measurement process.
True Value: The actual or accepted value of the quantity being measured.
Here are a few key points to consider:
Magnitude of Error: The relative error provides insight into how much the measured value deviates from the true value. A smaller relative error indicates a more accurate measurement, while a larger relative error indicates a less accurate measurement.
Unitless Measure: The relative error is expressed as a percentage, making it unitless. This allows for easy comparison across different measurements and quantities.
Direction of Error: The absolute value is taken in the numerator of the formula to ensure that the relative error is always positive, regardless of whether the measured value is greater or smaller than the true value.
Significance: The relative error takes into account the magnitude of the true value. For small true values, even a small absolute error might result in a relatively large relative error, and vice versa.
Percentage Representation: Multiplying by 100 converts the relative error into a percentage, which is often more intuitive and easier to interpret.
Comparison and Evaluation: Relative errors are often used to compare the performance of different measurement techniques, instruments, or methods. It can also help evaluate the accuracy and precision of a particular instrument.
It's important to note that the relative error is a measure of accuracy and does not capture the precision of a measurement. Precision refers to the repeatability of measurements and how closely repeated measurements cluster around the same value.
In some cases, it's also common to express the relative error in terms of fractions rather than percentages. This can be done by dividing the absolute error by the true value instead of multiplying by 100%.
Keep in mind that measurement and instrumentation involve various types of errors, including systematic errors, random errors, and instrumental errors. The relative error primarily addresses the random or random-like components of measurement error. To comprehensively assess the accuracy and precision of a measurement, it's important to consider these other sources of error as well.