Mathematical Formula For Calculating Percentage Error
\[ \text{Percentage Error} = \frac{\left| \text{Measured Value} – \text{Actual Value} \right|}{\text{Actual Value}} \times 100 \]
Example Broken Down With Steps
$$
\text{Given: True Value = 50, Measured Value = 45}
$$
$$
\text{Step 1: Subtract 45 from 50: } 50 – 45 = 5
$$
$$
\text{Step 2: Divide 5 by 50: } \frac{5}{50} = 0.1
$$
$$
\text{Step 3: Multiply 0.1 by 100: } 0.1 \times 100 = 10
$$
$$
\text{Result: Percentage Error is 10%.}
$$
Further Explained
Example: The true value is 50, and the measured value is 45.
Steps:
- Find the absolute difference: Subtract the measured value from the true value:
$$ 50 – 45 = 5 $$ - Divide the difference by the true value:
$$ \frac{5}{50} = 0.1 $$ - Convert to a percentage: Multiply the result by 100:
$$ 0.1 \times 100 = 10\% $$ - Conclusion: The percentage error is 10%.