Percent Error Calculator
Calculate percent error, absolute error, and relative error between experimental and theoretical values.
Enter experimental and theoretical values.
How Does the Formula Work?
Percent error quantifies the accuracy of a measurement by comparing an experimental (measured) value to a theoretical (accepted or true) value. It is a basic concept in science and engineering; used in lab reports, quality control, and calibration procedures to evaluate how close a measurement is to the expected result.
Related measures:
Absolute Error = |Experimental − Theoretical|
Relative Error = |Experimental − Theoretical| / |Theoretical|
Signed Error = (Experimental − Theoretical) / |Theoretical| × 100
Example: Measured gravity = 9.7 m/s², Accepted = 9.81 m/s²
Absolute Error = |9.7 − 9.81| = 0.11 m/s²
Relative Error = 0.11 / 9.81 = 0.01121
Percent Error = 0.01121 × 100 = 1.12%
Absolute vs Relative vs Percent Error
Absolute error gives the raw magnitude of the difference in the original units; useful when you need to know "how far off" in concrete terms. Relative error normalizes by the theoretical value, making it unitless and allowing comparison across different scales. Percent error is simply relative error expressed as a percentage for easier interpretation. A measurement off by 2 grams has an absolute error of 2 g; but whether that is significant depends on whether you are measuring 10 g (20% error) or 10 kg (0.02% error). Relative and percent error capture this context.
Signed vs Unsigned Error
Standard percent error uses absolute value and is always positive; it tells you the magnitude of the error but not the direction. Signed percent error preserves the sign: positive means overestimation (experimental higher than theoretical), negative means underestimation. In calibration and quality control, the direction of error matters; a thermometer that consistently reads 2° too high has a systematic positive bias that can be corrected, while random errors that go both ways indicate precision issues.
Quality Thresholds
The acceptable percent error depends on your course, lab manual or specification, and no single limit fits every case. The calculator assigns quality labels on its own scale; "Excellent" for ≤1%, "Good" for ≤5%, "Acceptable" for ≤10%, and "High error" above 10%; as a quick visual guide only. These cut-offs are a rule of thumb of this tool, not a standard, so check the limit that applies to your work.
When Theoretical Value Is Zero
Percent error is undefined when the theoretical value is zero because of division by zero. In this case, the calculator shows Undefined for the percent, relative and signed errors, with no quality label, and still gives the absolute error and the difference. Alternative metrics like absolute error or mean absolute error should be used instead. Some fields use a modified formula with the average of experimental and theoretical in the denominator, but this is not the standard definition and produces different results.
Tips & Recommendations
Green (≤1%), yellow (≤5%), orange (≤10%), red (>10%). Quick visual assessment of measurement quality.
See if your measurement is too high (+) or too low (−). Useful for detecting systematic bias in instruments or procedures.
View the complete formula breakdown showing how the percent error was calculated; useful for homework and lab reports.
Absolute, relative, percent, and signed; four complementary measures of error from a single calculation.
Frequently Asked Questions
What is percent error?
Percent error measures how far an experimental (measured) value is from a theoretical (accepted) value, expressed as a percentage. Formula: |experimental − theoretical| / |theoretical| × 100.
What is the difference between absolute and relative error?
Absolute error is the raw difference |exp − theo| in the same units as the values. Relative error divides by the theoretical value to give a unitless ratio. Percent error is relative error × 100.
What does signed error mean?
Signed error keeps the direction: positive means the experimental value is higher than theoretical, negative means it is lower. Regular percent error uses absolute value and is always positive.
What if the theoretical value is zero?
When the theoretical value is zero, percent error is undefined (division by zero). The calculator then shows Undefined for the percent, relative and signed errors, gives no quality label, and still shows the absolute error and the difference. Use absolute error instead when the theoretical value is zero.
What is a good percent error?
It depends on your course, lab manual or specification. The calculator color-codes results on its own scale: green (≤1%), yellow (≤5%), orange (≤10%), red (>10%). These cut-offs are a rule of thumb of this tool, not a standard.
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