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Reviewed by CA Divyanshu Sengar · Last reviewed 11 October 2026
Find the sample size for a test of controls when you expect no deviations, then enter what you found to see the upper bound of the population deviation rate and whether it stays within your tolerable rate.
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The sample used to test the operating effectiveness of a control differs from a sample aimed at measuring rupee misstatements in an account balance. This calculator is an illustrative attribute/deviation-rate model. It is explicitly not a substantive monetary unit sampling tool, nor an ICAI-prescribed numerical method. SA 530 requires auditors to select sampling units and sample sizes responsive to the purpose and risk of the procedure.
Under the simplifying independent-with-replacement binomial assumption, the probability of observing no exceptions in n tests is (1 – true deviation rate) to the power n. To achieve a selected one-sided confidence at a tolerable deviation rate, solve n using logarithms. At a 5% tolerable deviation rate and 95% confidence, the zero-exception model produces a sample of 59. That result does not justify 59 samples if expected deviations, population risk, strata or other design facts differ.
Where tested units and observed deviations are entered, the engine calculates an exact one-sided binomial upper confidence bound on the underlying deviation probability. If the upper bound exceeds the tolerance chosen by the audit team, the result flags escalation. A statistical conclusion is not a final control effectiveness decision; exceptions must be investigated, and non-sampling errors or biases remain possible.
Define the control and population, ascertain completeness, choose the sampling unit, evaluate expected error, select items without biased substitution, keep evidence of the selection method and investigate each deviation. If the audit requires a monetary substantive sample, use a separately validated method, including tolerable misstatement and expected misstatement. Never present the statistical confidence result as absolute certainty.
The displayed planning number assumes that observing no exceptions is the desired design. If a control historically fails, the auditor may not be able to support reliance merely by increasing the number of observations. Expected deviation, tolerable deviation, selection technique and alternative evidence need attention before choosing a sample. Lower tolerable deviation or higher confidence increases the mathematical sample under the selected model; these values must come from documented engagement judgment.
The upper bound estimates a conservative upper population deviation rate under the assumed statistical model and observed results. It is not an estimate of rupee misstatement and does not independently establish that the population or sampling frame was complete. If a selected transaction was not available for audit, the auditor must consider its treatment in the sample and whether the procedure is adequate. Sampling outside the control’s operating period may invalidate conclusions regardless of the calculated confidence percentage.
With no deviations expected, 59 clean items give 95% confidence that the true deviation rate is below 5%, because 0.95^59 is about 0.049.
The upper bound rises above 5% (about 7.8%), so the model flags escalation. You may need a larger sample or alternative procedures.
That is the mathematical zero-exception binomial plan under the displayed assumptions.
No. The audit conclusion must incorporate sample design, control facts and qualitative evidence.
No. That requires a differently scoped audit sampling model.
Rates and rules were checked against these sources on 11 October 2026. Notifications and standards change; confirm on the official site before you file, book or advise.
Educational working tool. Results follow the scope and assumptions above and the figures you enter; they are not tax, audit, legal or accounting advice. Tax and accounting treatment depends on facts and on the law or standard in force for the relevant period, so verify the official source or consult a professional before you rely on a result.
Background, worked examples and the rules behind these numbers.