Percent Error

Measuring How Far a Result Strayed From the Expected Value

Percent error measures how far a measured (experimental) value is from a known, accepted (theoretical) value, expressed as a percentage. It’s the standard way science labs and measurement-based fields report how accurate a result was. Enter both values, and this calculator finds the percent error instantly.

The Formula

$$\text{Percent Error} = \frac{\left|\vA{\text{Experimental}} - \vB{\text{Theoretical}}\right|}{\left|\vB{\text{Theoretical}}\right|} \times 100$$

The result is always reported as a positive percentage — percent error measures the SIZE of the error, not its direction. Whether your experimental value came in above or below the theoretical one, this calculator’s analysis notes which way it went.

Worked Example

An experiment measures a value of 48, when the accepted theoretical value is 50:

1. Difference: $48 - 50 = -2$
2. Percent error: $|-2| \div |50| \times 100 = 4\%$

Percent Error vs. Percent Difference

Percent error and percent difference sound similar but answer different questions. Percent error compares a measurement against a known, accepted “correct” value — use it whenever you have a true or theoretical value to compare against. Percent difference (available on this site’s Percentage Calculator) instead compares two measurements to each other with no assumption that either one is “correct,” dividing by their average rather than a single accepted value.

Key Factors to Consider

• A smaller theoretical value can produce a misleadingly large percent error for the same absolute difference. Since percent error divides by the theoretical value, an identical absolute error (say, 2 units) produces a much larger percent error against a small theoretical value than against a large one — worth keeping in mind when comparing percent errors across measurements of very different scales.
• Systematic and random error are two different sources behind a nonzero percent error, and they call for different fixes. A systematic error (like a miscalibrated instrument) consistently pushes results in the same direction, while random error varies unpredictably from trial to trial — repeating a measurement multiple times and averaging helps reduce random error, but won’t fix a systematic bias in the equipment or method itself.
• What counts as an “acceptable” percent error varies enormously by field. A physics experiment measuring a well-established constant might expect well under 1% error, while some biological or environmental measurements routinely see percent errors in the double digits due to natural variability — there’s no single universal threshold for what counts as a “good” result.
• Percent error assumes the theoretical value itself is genuinely correct. If the accepted “theoretical” value used for comparison is itself outdated or inaccurate, a low percent error against it doesn’t guarantee the experimental measurement is actually close to physical reality — the theoretical reference matters as much as the measurement being checked.

Common Mistakes

• Using percent error when neither value is actually a known “correct” reference. If you’re comparing two independent measurements with no accepted true value, percent difference (on the Percentage Calculator calculator) is the right tool, not percent error — dividing by a value that isn’t genuinely authoritative gives a misleading result.
• Forgetting to take the absolute value before comparing across experiments. Percent error is always reported as a positive size of the error — treating a negative raw difference as the final answer, or comparing signed differences across experiments, confuses “how far off” with “which direction,” which are two separate questions this calculator answers separately.
• Assuming a low percent error alone proves a measurement is trustworthy. A small percent error only says the result is close to the stated theoretical value — if that reference value is itself wrong or the measurement technique has an undetected systematic bias, a low percent error can still be misleading.

Useful to Know

• Comparing two measurements with no single accepted “correct” value between them? Percentage Calculator computes percent difference instead, which doesn’t assume either value is authoritative.
• Need to summarize error or variation across a whole set of repeated measurements, not just one comparison? Statistics Calculator computes mean, standard deviation, and other summary statistics from a full list of values.