Audit Sampling Size Calculator

ANA›Life Services Authority›National Calculator Authority›Audit Sampling Size Calculator

.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }

Audit Sampling Size Calculator

Calculate the statistically required sample size for audit procedures using classical variables or attribute sampling methods.

Sampling Method

Attribute Sampling (Rate of Occurrence) Variables Sampling (Monetary Amounts)

Confidence Level (%)

90% 95% 98% 99%

Expected Error Rate (%)

Tolerable Error Rate (%)

Population Book Value ($)

Tolerable Misstatement ($)

Expected Misstatement ($)

Estimated Standard Deviation ($)

Population Size (items, 0 = infinite)

Calculate Sample Size

function audToggleMethod() { var method = document.getElementById('aud-method').value; document.getElementById('aud-attribute-inputs').style.display = (method === 'attribute') ? '' : 'none'; document.getElementById('aud-variables-inputs').style.display = (method === 'variables') ? '' : 'none'; document.getElementById('aud-result').innerHTML = ''; }

function audCalc() { var resultDiv = document.getElementById('aud-result'); var method = document.getElementById('aud-method').value; var z = parseFloat(document.getElementById('aud-confidence').value); var N = parseFloat(document.getElementById('aud-population-size').value); var errors = []; var n, details;

if (method === 'attribute') { var p = parseFloat(document.getElementById('aud-expected-rate').value) / 100; var te = parseFloat(document.getElementById('aud-tolerable-rate').value) / 100;

if (isNaN(p) || p = 1) errors.push('Expected Error Rate must be between 0.01% and 99.99%.'); if (isNaN(te) || te = 1) errors.push('Tolerable Error Rate must be between 0.1% and 50%.'); if (!errors.length && p >= te) errors.push('Expected Error Rate must be less than Tolerable Error Rate.'); if (errors.length) { resultDiv.innerHTML = '' + errors.join('') + '

'; return; }

// Attribute sampling formula: n = z² * p * (1-p) / e² // where e = te - p (precision = tolerable - expected) var e = te - p; var n_inf = (z * z * p * (1 - p)) / (e * e);

// Finite population correction: n_adj = n_inf / (1 + n_inf/N) if (N > 0 && !isNaN(N)) { if (N ' + 'ParameterValue' + 'Z-score (confidence)' + z.toFixed(3) + '' + 'Expected Error Rate (p)' + (p * 100).toFixed(2) + '%' + 'Tolerable Error Rate (te)' + (te * 100).toFixed(2) + '%' + 'Precision (te - p)' + (e * 100).toFixed(2) + '%' + 'Infinite Population n' + Math.ceil(n_inf) + '' + (N > 0 ? 'Population Size (N)' + N.toLocaleString() + '' : '') + 'Required Sample Size' + n + '' + '';

} else { var BV = parseFloat(document.getElementById('aud-population-value').value); var TM = parseFloat(document.getElementById('aud-tolerable-misstatement').value); var EM = parseFloat(document.getElementById('aud-expected-misstatement').value); var SD = parseFloat(document.getElementById('aud-std-dev').value);

if (isNaN(BV) || BV = TM) errors.push('Expected Misstatement must be less than Tolerable Misstatement.'); if (!errors.length && TM > BV) errors.push('Tolerable Misstatement cannot exceed Population Book Value.'); if (errors.length) { resultDiv.innerHTML = '' + errors.join('') + '

'; return; }

// Variables sampling (mean-per-unit / difference estimation): // Precision A = TM - EM (allowance for sampling risk) // n_inf = (z * SD * sqrt(N_eff) / A)² but simplified for mean-per-unit: // n = (z * SD / (A / N))² where A/N is precision per unit // More precisely: n_inf = (z² * SD²) / (precision_per_unit²) // precision_per_unit = (TM - EM) / N_eff // For unknown N, use ratio: n = (z * SD * BV / (TM - EM))² / BV -- simplified // Standard formula: n = (z * N * SD)² / ((TM - EM)² + z² * SD²) with finite correction built in // Using: n_inf = (z * SD / ((TM - EM) / sqrt_N))^2 requires N // Best practice formula (AICPA): n = z² * SD² * N² / ((TM-EM)² * N + z² * SD²) -- requires N // If N unknown, use: n = (z * SD / ((TM-EM)/sqrt(N_proxy)))^2 // The standard mean-per-unit formula with finite correction when N is given: // n_inf = (z * SD / e_bar)^2 where e_bar = (TM - EM) / N_items // Since N may be 0, estimate N_items from BV if not given

var N_items = (N > 0 && !isNaN(N)) ? N : Math.round(BV / (BV / 1000)); // fallback estimate if (N ' + 'ParameterValue' + 'Z-score (confidence)' + z.toFixed(3) + '' + 'Population Book Value$' + BV.toLocaleString() + '' + 'Tolerable Misstatement$' + TM.toLocaleString() + '' + 'Expected Misstatement$' + EM.toLocaleString() + '' + 'Precision (TM - EM)$' + precision.toLocaleString() + '' + 'Std Deviation per Item$' + SD.toLocaleString() + '' + 'Population SizeNot provided (infinite assumed)' + 'Required Sample Size' + n + '' + ''; } else { if (N ' + 'ParameterValue' + 'Z-score (confidence)' + z.toFixed(3) + '' + 'Population Book Value$' + BV.toLocaleString() + '' + 'Population Size (N)' + N.toLocaleString() + '' + 'Tolerable Misstatement$' + TM.toLocaleString() + '' + 'Expected Misstatement$' + EM.toLocaleString() + '' + 'Precision (TM - EM)$' + precision2.toLocaleString() + '' + 'Precision per Unit (ē)$' + e_bar.toFixed(4) + '' + 'Std Deviation per Item$' + SD.toLocaleString() + '' + 'Infinite Population n' + Math.ceil(n_inf_v2) + '' + 'Required Sample Size' + n + '' + ''; } }

// Cap sample at population size if finite var cappedNote = ''; if (N > 0 && !isNaN(N) && n >= N) { n = N; cappedNote = 'Note: Required sample equals or exceeds population size. A 100% examination is recommended.

'; }

resultDiv.innerHTML = '### Result: Required Sample Size = ' + n + ' items ' + details + cappedNote; }

#### Formulas Used

Attribute Sampling (infinite population):

n = Z² × p × (1 − p) / (te − p)²

Where: Z = z-score for confidence level, p = expected error rate, te = tolerable error rate

Attribute Sampling (finite population correction):

n_adj = n / (1 + n / N)

Variables Sampling — Mean-Per-Unit (with population count N):

n = Z² × σ² / ē²   where   ē = (TM − EM) / N

With finite correction: n_adj = n / (1 + n / N)

Variables Sampling — Ratio Estimation (without population count):

n = Z² × σ² × BV / (TM − EM)²

Where: σ = standard deviation per item, BV = population book value, TM = tolerable misstatement, EM = expected misstatement

#### Assumptions & References

• References: AICPA Audit Sampling Guide (2014); ISA 530 — Audit Sampling; PCAOB AS 2315; Arens, Elder & Beasley, Auditing and Assurance Services.

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Study Time Planner Authority Network America › Life Services Authority › National Calculator Authority .calc-container { max-width: 640px;...

References

• 10 CFR § 26.41 — § 26.41 Audits and corrective action.
• 10 CFR § 26.415 — § 26.415 Audits.
• 10 CFR § 71.137 — § 71.137 Audits.
• 10 CFR § 72.176 — § 72.176 Audits.