MUS sample sizes are derived from Poisson reliability factors - statistically valid and auditable under GAAS, PCAOB, and ISA sampling standards.
Audit, Compliance & Controls
Monetary unit sampling calculator that produces sample size, interval, and projected misstatement.
Enter population size, tolerable misstatement, confidence level, and expected error rate to calculate MUS sample size, sampling interval, and upper error limit for audit planning.
Direct answerMUS sample size = (population x reliability factor) / tolerable misstatement. The sampling interval = population / sample size. Items larger than the interval are automatically selected in full.
Sample sizeSampling intervalUpper error limit
1. Enter sampling parameters
CalculatorEnter the population balance, tolerable misstatement, confidence level, and expected error rate to size the sample.
Enter sampling parameters or load a sample to calculate MUS results.
Live Tool
Monetary Unit Sampling Calculator in the browser
Enter population and risk parameters to calculate MUS sample size, sampling interval, and projected misstatement.
Privacy-first workflow
This page runs in the browser and does not upload any data.
What this tool is built to solve
A monetary unit sampling calculator determines sample size and interval from population characteristics and risk parameters, then evaluates results against tolerable misstatement.
Items exceeding the sampling interval are always selected, ensuring the largest balances receive 100% coverage without manual stratification.
After testing, the UEL is compared to tolerable misstatement to reach a statistical conclusion about the population balance.
Key signals
Review sample size and interval before beginning selection to confirm the parameters are reasonable for the population.
Sampling observations
Observations about the sampling design based on the parameters entered.
Sampling plan detail
Full MUS calculation detail for inclusion in the audit sampling workpaper.
Sample size is calculated using Poisson reliability factors for the selected confidence level and expected error rate.
The sampling interval determines the skip distance for systematic dollar-unit selection across the population.
Compare expected error to tolerable misstatement to validate that the sampling design has an adequate precision buffer.
All sampling parameters in one place, ready for inclusion in the audit sampling planning workpaper.
Guide Below The Tool
How to use the MUS calculator well
A monetary unit sampling calculator applies Poisson reliability factors to calculate a statistically valid sample size for testing dollar-value populations in financial statement audits.
External auditors, internal auditors, and audit seniors sizing samples for accounts receivable, accounts payable, inventory, revenue, or other transaction populations where dollar-value weighting is appropriate.
The relationship between tolerable misstatement and expected misstatement determines the precision of the sample. Expected error should never exceed 50% of tolerable misstatement - if it does, the population likely contains errors and MUS may not be appropriate.
Workflow
Four practical steps
1
Define the population and obtain the book value.The population is the total dollar amount of the account or transaction class being tested. Exclude items to be tested 100% (e.g., items above a stratification threshold) from the MUS population.
2
Set tolerable misstatement based on audit materiality.Tolerable misstatement is typically set at performance materiality. For MUS, it represents the maximum dollar misstatement that could exist in the population without affecting the audit conclusion.
3
Select the confidence level and expected error rate.95% confidence is standard for high-risk populations; 90% for lower-risk. Expected error rate should be based on prior-year results or preliminary analytical procedures - never set to zero if errors are expected.
4
Apply the sampling interval to systematically select sample items.Start with a random number within the interval and select every nth dollar unit. The transaction containing that dollar unit is selected. Record the transaction, its book value, and audited value for each sample item.
Reliability factors come from the Poisson distribution. Common values: 95% confidence, 0 errors expected = 3.00; 90% confidence, 0 errors = 2.31; 95% confidence, 1 error expected = 4.75.
Items larger than the sampling interval are automatically included in the sample. If many items exceed the interval, consider reducing the population by separately selecting and testing these large items 100%.
When errors are found, the misstatement amount is expressed as a tainting percentage (error / book value). The tainting factor is applied to the sampling interval to project the error to the population.
After testing, calculate the UEL = basic precision + incremental allowance for misstatements found. If UEL exceeds tolerable misstatement, the population cannot be accepted without modification.
If no errors are found, the UEL equals the basic precision: (population x reliability factor) / sample size. This is the statistical maximum that could still be in the population at the selected confidence level.
Document population, tolerable misstatement, confidence level, reliability factor, sample size calculation, sampling interval, selection method, and evaluation conclusion in the audit workpaper.
The functional tool stays on top so auditors can size samples immediately without reading the methodology guide.
Sample size, interval, and upper error limit are presented simultaneously so the full sampling plan is visible in one place.
Ledger Summit can build a full audit sampling management tool or automated workpaper system, but this page delivers value now.
FAQ
Monetary Unit Sampling Calculator questions, answered directly
Monetary unit sampling (MUS), also called probability-proportional-to-size (PPS) sampling, is an audit sampling technique where each individual dollar in a population has an equal probability of being selected. Larger items have a higher probability of selection because they contain more dollar units.
MUS sample size is calculated as: n = (population x reliability factor) / tolerable misstatement. The reliability factor comes from the Poisson distribution and depends on the desired confidence level and expected number of errors. Common reliability factors: 95% confidence = 3.00 (0 errors), 90% = 2.31.
The sampling interval (also called the skip interval) is calculated as: population / sample size. Every nth dollar unit in the population is selected. Items larger than the interval are automatically selected in full.
No. The calculator runs entirely in your browser and does not send any data to a server.
Next Step
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