Percentage Error Calculator
Compares an experimental (observed) value to a theoretical (true) value.
This is a worked example. Clear the fields and enter your own values, then press Calculate.
PERCENTAGE ERROR
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Percentage Error Calculator
Percentage Calculators
Percentage error measures how far an experimental or observed value strays from a known theoretical or true value, which is a core calculation in lab work, engineering, and any field that compares a measurement against an accepted standard. This percentage error calculator takes your experimental and theoretical values and returns the percentage error along with the full solution, so you can show your work rather than just reporting a final number.
How to use this percentage error calculator
- Enter your Experimental Value, the observed or measured result.
- Enter your Theoretical Value, the known, accepted, or true value you’re comparing against.
- Click Calculate to see the Percentage Error and the full Solution steps.
- Click Clear to reset both fields.
What this percentage error calculator does
Unlike percentage difference, which treats two values as equals, percentage error specifically compares an experimental (observed) value against a theoretical (true) value, meaning the two inputs are not interchangeable. The theoretical value is always the base of the calculation, since it represents the accepted or expected result that the experimental value is being measured against.
The percentage error formula
Percentage Error = |Experimental − Theoretical| ÷ |Theoretical| × 100
The numerator is the absolute difference between what you observed and what was expected. The denominator is the absolute value of the theoretical value specifically, not an average of the two, which is what makes this calculation directly comparable across different experiments even when the theoretical values themselves are very different in size.
Why the theoretical value is the base
Because percentage error is meant to show how far off a measurement is relative to a known correct answer, the theoretical value has to be the reference point, not the experimental one. Swapping which value you call “experimental” and which you call “theoretical” changes the result, since the denominator would then be based on a different number, unlike a percentage difference calculation where the two values are interchangeable.
Reading a percentage error result
| Result range | General interpretation |
|---|---|
| 0% | The experimental value exactly matches the theoretical value |
| Small percentage (typically under 5%) | Often considered acceptable measurement error in many scientific and engineering contexts, though the acceptable threshold varies by field |
| Larger percentage | Suggests a measurement issue, systematic error, or a genuine discrepancy worth investigating further |
What counts as an acceptable percentage error depends entirely on the field and the specific experiment or measurement, so there’s no single universal cutoff. A chemistry lab measurement and an engineering tolerance check can have very different standards for what percentage error is considered within an acceptable range.
Percentage error versus percentage difference
These two calculations look similar but answer different questions. Percentage error assumes one value (theoretical) is correct and measures how far the other (experimental) value deviates from it. Percentage difference makes no such assumption, treating both values as equally valid and comparing them against their shared average instead. Use percentage error whenever you have a known correct or expected value to measure against, and percentage difference when you’re comparing two values with no clear “correct” answer between them.
Frequently asked questions
Which value goes in the Experimental field and which goes in Theoretical?
Experimental Value is what you actually observed or measured. Theoretical Value is the known, accepted, or expected value you’re comparing your measurement against. These are not interchangeable, since the theoretical value forms the base of the calculation.
Can percentage error be negative?
This calculator reports percentage error using an absolute value in the numerator, so the result shown is always zero or positive. Some fields do report a signed percentage error to indicate whether the experimental value was higher or lower than theoretical, but the magnitude calculated here reflects how far off the measurement was, regardless of direction.
What’s considered a “good” percentage error?
There’s no universal threshold. Acceptable percentage error varies significantly by field, the precision of the equipment used, and the nature of the experiment. A result that’s excellent in one context might be unacceptable in another, so compare your result against the standard expected for your specific type of measurement.