Percentage error \[p\%=\left(\frac{error}{correct value} \right) \times 100 \% \]
Percentage error is a measure of the accuracy of a measurement or calculation compared to the true or accepted value. It is calculated by taking the absolute difference between the measured value and the true value, dividing it by the true value, and then multiplying by 100 to express it as a percentage.
Percentage Error = (Measured Value - True Value) / True Value * 100
Where measured value is the experimental value and the true value is the original value.
Suppose a student measures the length of a table to be 120 cm, but the actual length is known to be 125 cm. The percentage error can be calculated as follows:
Percentage Error = Measured Value - True Value/ True Value 100
= 120 cm - 125 cm / 125 cm 100
= -5 cm / 125 cm * 100
= - 4%
An experiment is conducted to determine the density of a liquid. The accepted value for the density is 1.2 g/mL, but the measured value obtained by the student is 1.3 g/mL.
The percentage error can be calculated as follows:
Measured Value - True Value / True Value 100
= (1.3 g/mL - 1.2 g/mL) / 1.2 g/mL 100
= 0.1 g/mL / 1.2 g/mL * 100
= 8.33%
A scientist performs a calculation to determine the velocity of an object. The accepted value for the velocity is 50 m/s, but the calculated value obtained by the scientist is 45 m/s.
= Calculated Value - True Value / True Value 100
= (45 m/s - 50 m/s) / 50 m/s 100
= (5 m/s )/( 50 m/s) * 100
= 10%
