Percentage error shows how much a measured (observed) value deviates from a true (accepted) value as a percentage. A smaller percentage indicates measurements are closer to the true value, while a larger percentage suggests more deviation.

Formulas:

• Absolute Error: $$\text{Absolute error} = \big|V_{\text{observed}} - V_{\text{true}}\big|$$
• Relative Error: $$\text{Relative error} = \frac{\big|V_{\text{observed}} - V_{\text{true}}\big|}{\big|V_{\text{true}}\big|}$$
• Percentage Error: $$\text{Percentage error} = \frac{\big|V_{\text{observed}} - V_{\text{true}}\big|}{\big|V_{\text{true}}\big|} \times 100\%$$

Example: If the observed value is 56.891 and the true value is 62.327:

$$\text{Percentage error} = \frac{|56.891 - 62.327|}{62.327} \times 100\% \approx 8.722\%$$

Optional signed percentage error (retaining negative sign to show direction):

$$\text{Signed percent error} = \frac{V_{\text{observed}} - V_{\text{true}}}{|V_{\text{true}}|} \times 100\%$$