Percent Error Calculator
Free Percent error Calculator for percentages. Enter values to get step-by-step solutions with formulas and graphs. Get results you can export or share.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Percent Error = (|Experimental - Theoretical| / |Theoretical|) x 100
Where Experimental is the measured or observed value and Theoretical is the known, accepted, or true value. The absolute value ensures the result is always positive. The result represents how far off the measurement is as a percentage of the true value.
Worked Examples
Example 1: Gravitational Acceleration Measurement
Problem:A student measures gravitational acceleration as 9.75 m/s squared. The accepted value is 9.81 m/s squared. What is the percent error?
Solution:Absolute Error = |9.75 - 9.81| = 0.06 m/s squared\nPercent Error = (0.06 / 9.81) x 100\n= 0.006116 x 100\n= 0.6116%\nSigned Error = (9.75 - 9.81) / 9.81 x 100 = -0.6116%\nAccuracy = 100 - 0.6116 = 99.39%
Result:Percent error: 0.61% (underestimate, 99.39% accurate)
Example 2: Chemical Concentration Measurement
Problem:A titration yields a concentration of 0.105 M. The true concentration is 0.100 M. Find the percent error.
Solution:Absolute Error = |0.105 - 0.100| = 0.005 M\nPercent Error = (0.005 / 0.100) x 100\n= 0.05 x 100\n= 5.00%\nSigned Error = (0.105 - 0.100) / 0.100 x 100 = +5.00%\nAccuracy = 100 - 5.00 = 95.00%
Result:Percent error: 5.00% (overestimate, 95.00% accurate)
Frequently Asked Questions
What is percent error and why is it important?
Percent error measures the accuracy of a measurement by comparing an experimental or observed value to a known or accepted theoretical value. The formula is: Percent Error = (|Experimental - Theoretical| / |Theoretical|) x 100. It expresses the magnitude of error as a percentage of the true value, providing context for how significant the discrepancy is. A 5 gram error is trivial when measuring 10,000 grams (0.05% error) but catastrophic when measuring 10 grams (50% error). Percent error is fundamental in chemistry, physics, engineering, and any field that relies on precise measurements. It helps scientists evaluate experimental methods, identify systematic errors, and determine whether results meet acceptable accuracy thresholds.
What is the difference between percent error and percentage difference?
Percent error and percentage difference serve different purposes and use different denominators. Percent error compares a measured value to a known true value, using the true value as the denominator. Percentage difference compares two values of equal standing where neither is considered the reference standard, using their average as the denominator. If you measure gravity and get 9.75 m/s squared while the accepted value is 9.81 m/s squared, use percent error (0.61%). If two labs both measure an unknown quantity and get 9.75 and 9.87, use percentage difference (1.22%). The key distinction is whether one value is the accepted or true value. Using the wrong metric can misrepresent the reliability of measurements and experimental findings.
What is an acceptable percent error in scientific experiments?
Acceptable percent error varies dramatically by field and application. In introductory physics or chemistry labs, 5-10% error is generally acceptable. In analytical chemistry, errors under 1% are typically expected. In precision engineering and manufacturing, tolerances may require errors under 0.1% or even 0.01%. Pharmaceutical production demands extremely low percent errors due to safety implications. In social sciences and field measurements, errors of 5-15% may be acceptable due to inherent variability. The acceptable threshold depends on the measurement difficulty, available equipment, and consequences of error. Published scientific results typically report error alongside measurements, and reviewers evaluate whether the error is reasonable given the methodology used.
What causes high percent error in experiments?
High percent error in experiments can result from systematic errors, random errors, or both. Systematic errors create consistent bias in one direction, such as a miscalibrated instrument reading consistently high. Random errors cause unpredictable variations, such as reading a meniscus at slightly different angles. Human factors include incorrect measurement techniques, calculation mistakes, and misreading scales. Environmental factors like temperature fluctuations, air currents, and vibrations introduce error. Equipment limitations such as insufficient precision, worn components, or digital rounding contribute to error. Procedural issues like impure reagents, incomplete reactions, or timing errors are common in chemistry. Identifying the source of error is as important as quantifying it, because systematic errors can be corrected while random errors can only be minimized.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy