Estimate the confidence interval around an observed data-labeling accuracy rate. The calculator treats each reviewed label as a Bernoulli outcome—correct or incorrect—and uses the normal approximation to show a practical uncertainty range around the sample proportion.
This is useful when QA teams audit only part of a labeling batch and need to communicate how precisely the review sample represents the underlying labeling process. A narrower interval indicates more precision, while a wider interval signals that the observed accuracy could plausibly vary more in the full population. The result is most informative when the reviewed labels are sampled independently and are reasonably representative of the work being evaluated.
1. Enter the review size
Use the number of labels that were independently checked for correctness.
2. Enter correct labels
Provide the count that passed the review. It cannot exceed the number reviewed.
3. Choose a confidence level
Use the confidence level required for your reporting convention; 95% is a common default.
4. Read the interval
Compare the lower and upper bounds with your acceptance threshold, not just the point estimate.
Where:
Assumptions: The calculator uses a normal-approximation interval. With very small samples or rates near 0% or 100%, an exact or Wilson interval may be preferable.
The main result is the observed accuracy; the bounds show an approximate range consistent with the reviewed sample at the selected confidence level.
This is a sampling estimate, not a guarantee about every unlabeled or unreviewed item.
Given:
Calculation:
p = 460 / 500 = 0.92. Standard error = √(0.92 × 0.08 / 500) ≈ 0.01213. Margin = 1.96 × 0.01213 ≈ 0.02377.
Result:
Observed accuracy = 92.00%; approximate 95% interval = 89.62% to 94.38%.
Interpretation:
The audit suggests high accuracy, but the interval shows the uncertainty that remains because only a sample was reviewed.
Smaller samples contain less information about the underlying accuracy rate, so sampling uncertainty is larger. Increasing the number of independently reviewed labels generally narrows the interval.
Yes. A higher confidence level uses a larger critical value and therefore produces a wider interval for the same sample.
The normal approximation can understate uncertainty when the observed rate is exactly 0% or 100%. For boundary cases, consider a Wilson or exact binomial interval.
Only if the observations are being treated as independent. Multiple judgments on the same item may be correlated and can overstate the effective sample size.
Accuracy reports the share judged correct, while error rate reports the share judged incorrect. They sum to 100% when every reviewed item is classified as either correct or incorrect.