The formulas
- Weight = balance (or square root of balance)
- Allocated = performance materiality x weight / sum of weights
How it works
When sampling several accounts, the auditor sets tolerable misstatement for each. One simple approach is to spread a total in proportion to account size. The square-root basis is a judgment-based variant, not a requirement of the standards. It gives smaller accounts a larger share, so a small balance does not get an unusably small tolerance.
The total here is performance materiality, but the right total to allocate depends on the audit approach. Each allocated amount stays at or below performance materiality because the parts sum to it, and judgment decides the final numbers. Document the basis you pick.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
Why the square root?
It narrows the gap between large and small accounts so small accounts are not given a trivial tolerance.
Must the parts add to the whole?
Summing to performance materiality is the conservative choice and is what this tool does. Your firm methodology sets the actual rule.
Can I use it for components?
Yes, enter component balances instead of accounts.
Formulas on this page are the standard definitions.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.