The Percentage Error Formula
In scientific experiments and data analysis, percentage error quantifies how far an experimental observation deviates from a known or standard baseline value:
Percentage Error Formula
$$\text{Percentage Error} = \left| \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right| \times 100\%$$
Example (Measured = 9.8, True = 10):
$$\text{Error} = \left| \frac{9.8 - 10}{10} \right| \times 100\% = \left| \frac{-0.2}{10} \right| \times 100\% = \mathbf{2\%}$$
Percentage Error Reference Examples
Here are representative examples demonstrating how variations in measurement affect the final error percentage:
| Measured Value | True Value | Absolute Difference | Percentage Error |
|---|---|---|---|
| 9.8 m/s² | 9.80665 m/s² | 0.00665 | 0.0678% |
| 105 g | 100 g | 5 g | 5.00% |
| 18.5 cm | 20.0 cm | 1.5 cm | 7.50% |
| 45 mL | 50 mL | 5 mL | 10.00% |
Why Percentage Error Uses Absolute Values
Percentage error measures how far off a measurement is from the accepted true value, expressed as a percentage of that true value. Using the absolute value of the difference means the result is always reported as a positive percentage, regardless of whether the measurement came in above or below the true value — the direction can still be noted separately if it matters for the context.
How to Use This Calculator
- Enter the value you measured or calculated in the Measured value field.
- Enter the accepted true or theoretical reference in the True value field.
- The percentage error updates instantly in real time.
Frequently Asked Questions
How is percentage error calculated?
Subtract the true value from the measured value, take the absolute value of that difference, divide by the true value, then multiply by 100.
Why is the result always positive?
Because the formula uses the absolute value of the difference, so it reports the size of the error without indicating direction.
What counts as a 'good' percentage error?
This depends entirely on context — a 2% error might be excellent in one field and unacceptable in another where high precision is required.
What if my true value is zero?
Percentage error is undefined when the true value is zero, since the formula involves dividing by that value.