How this calculator works
Percent error compares an experimental or measured value against a known, accepted, or theoretical value, expressing the gap as a percentage. It's the standard way lab reports and quality-control checks quantify how close a measurement came to the expected answer.
This calculator returns both the absolute percent error, always a non-negative number, and the signed version, which keeps the direction of the mistake: positive means the measured value overshot the actual value, negative means it undershot. The direction label makes that distinction explicit without you needing to check the sign.
The formula
Percent error = |measured − actual| ÷ |actual| × 100Signed percent error = (measured − actual) ÷ |actual| × 100Dividing by the absolute value of the actual number keeps the percentage meaningful even when the actual (accepted) value itself happens to be negative, such as a temperature below zero.
Worked example: a chemistry lab density measurement
- A student measures the density of a liquid as 1.02 g/mL. The accepted (literature) density is 1.00 g/mL.
- Difference: 1.02 − 1.00 = 0.02.
- Percent error: 0.02 ÷ 1.00 × 100 = 2%.
- Since the measured value (1.02) is higher than the actual value (1.00), this is an overestimate.
Frequently asked questions
What is a "good" percent error?
It depends entirely on the field and the equipment being used. A percent error under 5% is often considered acceptable in an introductory chemistry lab, but precision instruments in other fields may expect error well under 1%. Always check what your course, lab manual, or industry standard expects.
What's the difference between percent error and percent difference?
Percent error compares a measured value against a known, accepted, or theoretical value. Percent difference compares two measured values where neither is treated as the definitive correct answer, and typically divides by the average of the two instead of by one of them.
Why take the absolute value?
Percent error is conventionally reported as a non-negative number, since the main question is usually how far off a measurement was, not which direction. This calculator also shows the signed version separately, for when the direction matters.
What happens if the actual value is 0?
Percent error is undefined when the actual value is 0, since the formula requires dividing by it. In that situation, consider reporting the plain absolute difference instead of a percentage.
Is percent error the same as accuracy?
Not exactly. Percent error is the specific number calculated from the formula |measured − actual| ÷ |actual| × 100, while accuracy is the broader, often qualitative idea of how close a measurement is to the truth. A lower percent error means a more accurate measurement, but percent error is the precise figure; accuracy is the general concept it quantifies.