Percent Error Calculator
Calculate the percentage error between actual and measured values
The true, accepted, or theoretical value
The value you obtained from measurement or experiment
How to Use This Calculator
Enter Actual Value
Type the theoretical, accepted, or true value (from reference books, known standards, etc.).
Enter Measured Value
Type the value you obtained from your experiment, measurement, or observation.
Interpret Results
The calculator shows percent error with color-coded accuracy indicators.
Formula
Percent Error = (|Measured Value - Actual Value| / |Actual Value|) × 100
Example 1: Measuring length
Actual length: 10.0 cm
Measured length: 9.7 cm
Error = (|9.7 - 10.0| / 10.0) × 100
Error = (0.3 / 10.0) × 100 = 3%
Low error - Good accuracy
Example 2: Chemistry experiment
Theoretical yield: 25.0 g
Experimental yield: 23.5 g
Error = (|23.5 - 25.0| / 25.0) × 100
Error = (1.5 / 25.0) × 100 = 6%
Moderate error - Acceptable
Example 3: Temperature measurement
Actual temperature: 100°C
Measured temperature: 105°C
Error = (|105 - 100| / 100) × 100
Error = (5 / 100) × 100 = 5%
Moderate error
About Percent Error Calculator
The Percent Error Calculator is an essential tool for scientists, students, and professionals who need to quantify the accuracy of measurements or experimental results. Percent error expresses the difference between a measured value and the actual (theoretical or accepted) value as a percentage, helping you assess the quality and reliability of your data.
When to Use This Calculator
- Science Experiments: Calculate error in lab measurements and experimental results
- Chemistry: Determine percent error in yields, concentrations, or reaction rates
- Physics: Assess measurement accuracy in experiments
- Engineering: Evaluate precision in specifications and measurements
- Quality Control: Monitor manufacturing accuracy and tolerances
- Academic Work: Complete lab reports and homework assignments
Why Use Our Calculator?
- ✅ Color-Coded Results: Visual indicators for error levels
- ✅ Shows Absolute Error: Displays both percent and absolute error
- ✅ Instant Calculation: Get results immediately
- ✅ 100% Accurate: Precise mathematical calculations
- ✅ Educational: Helps understand measurement accuracy
- ✅ Completely Free: No registration required
Understanding Percent Error
Percent error measures the accuracy of a measured value compared to the true or accepted value. A lower percent error indicates higher accuracy.
- 0% = Perfect accuracy (measured = actual)
- < 5% = Excellent accuracy (usually acceptable in most experiments)
- 5-10% = Good accuracy (acceptable for many applications)
- > 10% = Consider rechecking measurements or procedure
Real-World Applications
Chemistry Lab: In a synthesis experiment, the theoretical yield is 15.0 g but you obtained 14.2 g. The 5.33% error helps you evaluate your technique and procedure.
Physics Experiment: Using a spring scale, you measure acceleration due to gravity as 9.65 m/s² (actual: 9.81 m/s²). The 1.63% error indicates good experimental accuracy.
Manufacturing: A part should be 50.0 mm but measures 50.3 mm. The 0.6% error is within acceptable tolerances.
Tips for Reducing Percent Error
- Use calibrated, precision instruments
- Take multiple measurements and calculate the average
- Follow proper experimental procedures carefully
- Control environmental variables (temperature, humidity, etc.)
- Minimize human error through careful observation
- Record data accurately and precisely
Frequently Asked Questions
Can percent error be negative?
No. Percent error uses absolute values, so it's always positive. It measures the magnitude of error, not the direction.
What's an acceptable percent error?
It depends on the field and application. Generally, <5% is excellent, 5-10% is good, and >10% may need investigation. Always check your specific requirements.
What's 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 without a reference standard.
Can percent error exceed 100%?
Yes! If your measured value is very different from the actual value, percent error can exceed 100%. This indicates a significant measurement problem.
Which value should I enter first?
Enter the actual/theoretical value first, then the measured/experimental value. The formula uses absolute values, so the result is the same either way.