Where the extra cent goes
Three five-cent bases reveal a one-cent difference between line rounding and total rounding. Reproduce both methods and their negative mirrors.
Three tiny lines are enough to make two otherwise correct commission calculations disagree. Each has a five-cent basis and a 10% rate. Round every line and the answer is three cents. Combine the bases before rounding and it is two cents. The missing explanation is the point at which fractions of a cent become money.
Worked fictional example · amounts in AUD
The useful part
The one-cent difference comes from applying the same rounding rule at different stages. Record the rounding stage as well as the rate.
Your working files
Download the three-line experimentCSV · Five-cent bases, exact unrounded outputs and expected line-rounded results.A deliberately small experiment
The downloadable dataset contains R1, R2 and R3, each with a $0.05 basis. We use unusually small values to expose the mechanism without hiding it inside a large report. They are fictional arithmetic inputs, not plausible service prices. Tax is not part of this experiment: the five cents is already the agreed calculation basis.
At 10%, each unrounded result is $0.005000. That is half a cent. Trimsum’s calculation engine rounds exact half cents away from zero, so each positive line becomes $0.01. The dataset keeps the unrounded six-decimal value alongside the rounded money value; looking only at displayed cents would conceal the cause.
The same rate, two different stages
The line method produces $0.01 + $0.01 + $0.01 = $0.03. The total method first combines $0.05 + $0.05 + $0.05 = $0.15, then applies 10%, producing $0.015. Rounded once, that becomes $0.02. Neither method changed the source basis or the rate. The sequence changed.
| Method | Unrounded calculation | Rounded result |
|---|---|---|
| Each line | 3 × $0.005000 | $0.03 total |
| Combined basis | $0.15 × 10% = $0.015000 | $0.02 total |
| Difference | Line method less total method | $0.01 |
A refund should expose the same rule
Change all three bases to −$0.05. The line results become −$0.01 each, adding to −$0.03. The combined basis is −$0.15; 10% gives −$0.015, rounded to −$0.02. The difference is now −$0.01. The positive and negative experiments cancel exactly when their inputs are exact opposites.
This symmetry is a useful diagnostic. A method that rounds a positive half cent upward but a negative half cent toward zero can leave a residual when a transaction is fully reversed. Test the actual signed values rather than applying a positive-money formula and attaching a minus sign only when displaying the answer.
Why integer cents still need a rounding policy
Storing $0.05 as five cents avoids treating an imprecise binary decimal as the source amount. A rate of 10% can be represented as 1,000 basis points, with 10,000 representing 100%. The multiplication is therefore five times 1,000 divided by 10,000, yielding half a cent. Integer inputs do not make the fractional result disappear.
The public tools use integer arithmetic for this ratio, and the workspace engine uses the same half-away-from-zero policy. The calculation still needs an explicit moment at which the fraction is rounded. “We use cents” describes the representation; “we round each contributing line” describes the operational choice.
How to diagnose a larger report
When a real report differs by a small amount, keep the source lines intact and compare the two rounding stages before adding a balancing adjustment. Use the rounding tool with the same basis values and one common rate. If different staff or categories have different rates, separate those groups; adding unlike bases and applying one rate would answer a different question.
A result that matches the observed difference is a lead, not complete proof of the source system’s policy. Confirm which report calculated the commission and whether it rounded by line, invoice, person, category or whole period. Those intermediate groupings can generate their own differences.
Do not make a cent disappear with formatting
Reducing decimal places in a spreadsheet changes what you see, and may leave the underlying fractional values available to later formulas. Replacing a calculated value with a typed cent changes the data. Neither action documents why the two reports differed. Keep the original source result and the independently calculated result side by side.
The workspace flags reported differences larger than one cent. A one-cent difference is therefore not necessarily a review warning there. The public variance tool displays nonzero differences including one cent. That distinction matters when investigating this exact example: absence of a workspace warning does not mean both numbers are identical.
A test you can repeat in seconds
Enter 0.05 on three separate lines in the rounding comparison tool and use 10%. Expect $0.03 for line rounding, $0.02 for combined rounding and $0.01 for the difference. Then repeat with negative values. Keep the CSV if you need the experiment alongside a report explanation.
We checked the fixture with the actual engine ratio function and the public-tool test suite on 27 September 2026. The expected positive and negative results passed. This establishes the behaviour of this implementation for these inputs; it does not certify a provider’s report or decide which rounding arrangement your business should adopt.
Put it to work.
Inspect source rows, supplied rates and review decisions in the sample workspace.
Explore the sample close