Percent Error Calculator
Calculate the percent error between an experimental and theoretical value.
Essential for lab reports and evaluating the accuracy of measurements.
What Is Percent Error?
Percent error measures how close an experimental (measured) value is to a theoretical (accepted or true) value. It is expressed as a percentage and is fundamental to all experimental science — from high school chemistry labs to professional research.
The Formula
Absolute (unsigned) percent error:
Percent Error = |(Experimental − Theoretical) / Theoretical| × 100
Signed percent error (shows direction — positive means measured too high):
Percent Error = (Experimental − Theoretical) / Theoretical × 100
Supporting Calculations
Absolute Error = |Experimental − Theoretical|
Relative Error = |Experimental − Theoretical| / |Theoretical|
Percent Error = Relative Error × 100
Error vs. Mistake
An error in science is not a mistake — it refers to the unavoidable deviation between a measured value and the true value, caused by limitations of instruments, technique, or the measurement process itself. A mistake is a blunder (such as misreading an instrument), which should be corrected.
Types of Experimental Error
- Random error: Unpredictable fluctuations in either direction; reduced by taking multiple measurements and averaging
- Systematic error: Consistent bias in one direction (e.g., a miscalibrated scale always reads 5g too high); cannot be corrected by averaging
- Parallax error: Reading an instrument from the wrong angle
Accuracy Classification
| Percent Error | Accuracy Level |
|---|---|
| Below 1% | Excellent — publishable quality |
| 1% – 5% | Good — acceptable for most lab work |
| 5% – 10% | Acceptable — review technique and instruments |
| Above 10% | Poor — likely systematic error or blunder |
Percent Error vs. Percent Difference
These are different calculations:
- Percent error compares to a known theoretical value (one reference point)
- Percent difference compares two experimental values with no clear reference; uses the average as denominator
Worked Example
A student measures the density of aluminum and gets 2.65 g/cm³. The accepted value is 2.70 g/cm³.
- Absolute Error = |2.65 − 2.70| = 0.05 g/cm³
- Percent Error = |0.05 / 2.70| × 100 = 1.85% (Good accuracy)
- The measured value is below the theoretical value
Common Uses
- Chemistry: measuring the yield of a reaction vs. theoretical yield
- Physics: timing experiments, measuring gravitational acceleration (theoretical: 9.81 m/s²)
- Biology: measuring cell sizes, enzyme activity
- Engineering: prototype performance vs. design specification