# Absolute and Relative Error – Analytical Chemistry

Absolute and Relative errors signify the accuracy of results indicating the closeness of a measured value to the true value or accepted value. The absolute error indicates how big the error actually is, while the relative error indicates how big the error is in relation to the correct value.

The agreement between the result and the standard value is measured by accuracy. Either the true or the acceptable value must be known in order to determine accuracy.

## Absolute error

The absolute error of a measurement is the difference between the true and measured values.

E = Xi – Xt

Where, E = absolute error, Xi = measured value, Xt = true or accepted value

The sign of absolute error tells whether the data is low or high than the true value. A negative sign indicates the value is low while a positive value indicates the measured value is higher than the true value.

## Relative error

The relative error is a more useful quantity than an absolute error because it is often measured during analysis. Depending on the size of the object being measured, the relative error indicates how accurate the measurement is. The relative error is either measured in percentage or parts per thousand (ppt).

If relative error is expressed in percentage, then the expression is

If relative error is expressed in parts per thousand (ppt), then the expression is

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