Percent Error Calculator with Explanation
Calculate percent error with complete explanations. Learn the formula, understand measurement accuracy, and reduce experimental errors. Free calculator.
Quick Answer
Percent error = |(Experimental - Theoretical)| / |Theoretical| × 100%. Measures deviation between measured and accepted values. Lower percent error indicates higher accuracy. Essential for scientific experiments and quality control.
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Calculate With Full ToolWhat is Percent Error?
Percent error measures the difference between an experimental value and a theoretical or accepted value, expressed as a percentage of the theoretical value. It quantifies the accuracy of measurements and experiments, helping identify systematic errors.
How Percent Error Works
The calculation finds the absolute difference between experimental and theoretical values, divides by the theoretical value, and converts to a percentage. This standardized measure allows comparison of errors across different scales and units of measurement.
Importance in Science
Percent error is crucial for validating experimental results, comparing measurement methods, and improving experimental techniques. Lower percent error indicates higher accuracy and reliability of measurements, essential for scientific research and quality control.
Percent Error Formula
Percent Error = |(Experimental - Theoretical)| / |Theoretical| × 100%
Formula: Percent Error = |(E - T)| / |T| × 100%
Where: E = Experimental value, T = Theoretical value
Absolute Value: Ensures percent error is always positive
Good Accuracy: < 5% percent error
Acceptable: 5-10% percent error
Poor Accuracy: > 10% percent error
Step-by-Step Example
Example: Experimental = 9.8 m/s², Theoretical = 9.81 m/s² (gravity)
Step 1: Identify values: Experimental = 9.8, Theoretical = 9.81
Step 2: Calculate difference: 9.8 - 9.81 = -0.01
Step 3: Take absolute value: |-0.01| = 0.01
Step 4: Divide by theoretical: 0.01 ÷ 9.81 ≈ 0.00102
Step 5: Convert to percentage: 0.00102 × 100% = 0.102%
Step 6: Interpret: Excellent accuracy (< 1% error)
This example shows a very accurate measurement of gravitational acceleration. The 0.102% error indicates high precision in the experimental method, well within acceptable scientific standards.
Who Should Use This Calculator?
Scientists
Validate experimental results and accuracy
Students
Analyze lab experiments and measurements
Quality Control
Monitor manufacturing precision and tolerances
Engineers
Assess measurement accuracy and calibration
Frequently Asked Questions
What's the difference between percent error and percent difference?
Percent error compares an experimental value to a known theoretical value, while percent difference compares two experimental values. Percent error has a reference standard, while percent difference compares two measurements.
Why do we use absolute value in percent error?
Absolute value ensures percent error is always positive, representing the magnitude of error regardless of direction. This allows consistent comparison of accuracy across different measurements and experiments.
What causes high percent error?
High percent error can result from systematic errors (calibration issues), random errors (measurement variations), human error, environmental factors, or incorrect methodology. Identifying the source helps improve accuracy.
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