Percent Error Calculator
Calculate the percent error between an experimental (measured) value and a theoretical (accepted) value. Percent error quantifies how far off a measurement is from the true value, expressed as a percentage of the theoretical value.
How to Calculate Percent Error
- Subtract the theoretical value from the experimental value.
- Take the absolute value of the difference (this is the absolute error).
- Divide the absolute error by the absolute value of the theoretical value (this is the relative error).
- Multiply by 100 to get the percent error.
Formula
Percent Error = |Experimental - Theoretical| / |Theoretical| x 100%
Absolute Error = |Experimental - Theoretical|
Relative Error = Absolute Error / |Theoretical|
Example Calculation
A student measures the boiling point of water as 99.1 C. The accepted value is 100.0 C.
Step 1: Absolute Error = |99.1 - 100.0| = 0.9
Step 2: Relative Error = 0.9 / |100.0| = 0.009
Step 3: Percent Error = 0.009 x 100 = 0.9%
Percent Error Interpretation Table
| Percent Error | Interpretation |
|---|---|
| 0% - 1% | Excellent accuracy |
| 1% - 5% | Good accuracy |
| 5% - 10% | Acceptable for most experiments |
| 10% - 20% | Moderate error, review procedure |
| > 20% | Significant error, likely systematic issue |
Frequently Asked Questions
Can percent error be negative?
The standard formula uses absolute value, so percent error is always positive. However, some fields use signed percent error to indicate whether the measurement is above or below the true value.
What is the difference between percent error and percent difference?
Percent error compares a measured value to a known true value. Percent difference compares two measured values to their average when neither is considered the "true" value.
What if the theoretical value is zero?
Percent error is undefined when the theoretical value is zero because you would be dividing by zero. In such cases, use absolute error instead.
What causes percent error in experiments?
Common causes include instrument limitations, human reading errors, environmental factors (temperature, humidity), impure samples, and systematic calibration issues.
Is a lower percent error always better?
Generally yes. A lower percent error indicates the experimental result is closer to the accepted value. However, acceptable error depends on the field and precision requirements.