Percent Error Calculator
Result:
Welcome to our Percent Error Calculator. This tool calculates the percentage error between an actual (measured) value and a theoretical (expected) value, helping you assess measurement accuracy.
What is Percent Error?
Percent error measures the accuracy of a measurement by comparing the difference between actual and theoretical values as a percentage of the theoretical value.
Percent Error Formula
Percent Error = |Actual - Theoretical| / |Theoretical| × 100%
Understanding the Components
Actual Value: The measured or observed value
Theoretical Value: The expected or accepted value
Absolute Error: |Actual - Theoretical|
Percent Error: Error as percentage of theoretical
Applications
Laboratory experiments: Measurement accuracy
Engineering: Design tolerances
Quality control: Manufacturing precision
Scientific research: Data validation
Education: Experimental analysis
Step-by-Step Calculation
Example: Measured length = 9.8 cm, Actual length = 10.0 cm
Step 1: Identify values
Actual (measured) = 9.8 cm, Theoretical (expected) = 10.0 cm
Step 2: Calculate absolute error
Absolute Error = |9.8 - 10.0| = |-0.2| = 0.2 cm
Step 3: Apply percent error formula
Percent Error = (0.2 / |10.0|) × 100% = 2.0%
Result: The measurement has a 2.0% error
Interpreting Percent Error
Low Error (< 5%)
High accuracy measurement
Good precision
Acceptable for most applicationsMedium Error (5-15%)
Moderate accuracy
May need improvement
Depends on application requirementsHigh Error (> 15%)
Low accuracy measurement
Needs investigation
Systematic error likelyCommon Sources of Error
- Systematic errors: Consistent bias in measurements (calibration issues)
- Random errors: Unpredictable fluctuations (environmental factors)
- Human errors: Mistakes in reading or recording data
- Instrumental errors: Limitations of measuring devices
- Environmental factors: Temperature, humidity, pressure variations
Real-World Examples
Laboratory Measurement
Expected: 25.0 mL
Measured: 24.7 mL
Error: 1.2%
Excellent accuracyManufacturing Tolerance
Target: 50.0 mm
Actual: 49.5 mm
Error: 1.0%
Within tolerancePhysics Experiment
Theoretical: 9.8 m/s²
Measured: 10.2 m/s²
Error: 4.1%
Good experimental resultTips for Reducing Percent Error
- Calibrate instruments: Ensure measuring devices are accurate
- Multiple measurements: Take several readings and average them
- Control environment: Minimize external factors
- Proper technique: Follow standard measurement procedures
- Use appropriate instruments: Choose tools with sufficient precision
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