Rounding Methods: Half-Up vs. Banker's Rounding and Why Totals Don't Match
October 29, 2026
Rounding replaces a number with a nearby simpler one. The common rule (round half up) rounds 2.5 to 3 and 3.5 to 4. Round half to even (banker's rounding) rounds a tie to the nearest even number: 2.5 goes to 2, 3.5 to 4, 0.5 to 0, and 1.5 to 2. Truncation simply drops the extra digits (2.9 becomes 2). Round half down rounds ties toward zero.
The difference matters when you round many values. Take 0.5, 1.5, 2.5, and 3.5, whose exact sum is 8.0. Half-up rounds them to 1, 2, 3, and 4, summing to 10, an upward bias of 2. Half-even rounds them to 0, 2, 2, and 4, summing to 8, with no bias.
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With round-half-up, every tie moves up, so across a large dataset with many ties, the totals drift upward. With half-even, ties go up half the time and down half the time, so the errors cancel on average. That is why it is the default in the IEEE 754 floating-point standard, in many financial systems, and in some programming languages (such as Python's round() function and .NET's Math.Round by default). Excel's ROUND uses half-up (away from zero), so results can differ between programs. Check the rounding mode when a total doesn't match.
| Value | Half-up | Half-even | Truncate |
|---|---|---|---|
| 0.5 | 1 | 0 | 0 |
| 1.5 | 2 | 2 | 1 |
| 2.5 | 3 | 2 | 2 |
| 3.5 | 4 | 4 | 3 |
| Sum (exact 8.0) | 10 | 8 | 6 |
Line-by-Line vs. Total Rounding
Invoices often show a total that differs by a cent from the sum of rounded line items. Example: three items at $1.25 each with 7.5% sales tax. Tax per line = $0.09375, rounded to $0.09; three lines add up to $0.27. The tax on the subtotal of $3.75 = $0.28125, rounded to $0.28. Whichever method is used, the difference is a cent, but with thousands of transactions, it accumulates. Tax laws specify the method: some jurisdictions require per-invoice rounding, others per line. Accounting systems carry extra decimals internally and round only at the end, or distribute the rounding differences to the largest line.
Practical Guidance
Round only at the final step; keep full precision in intermediate calculations. Document the rounding rule for reports. When splitting an amount into parts that must sum to the total (such as $100 divided among 3 people), allocate the leftover cents deliberately: $33.33, $33.33, and $33.34. Percentages that sum to 99% or 101% in a table are a result of rounding; note it or adjust the largest one. For measurement, follow significant figure rules.
Rounding Direction in Contracts
Rounding up (ceiling) is used for billing minutes or for ordering materials, since you can't buy half a box. Rounding down (floor) applies to things like complete years of age. Specify the rule in agreements to avoid disputes.
Frequently Asked Questions
What is banker's rounding?
Round half to even: ties go to the nearest even digit.
Why does it reduce bias?
Ties round up and down equally often, so errors cancel.
Why do rounded line items not match the total?
Rounding each item separately accumulates differences from rounding the sum.
When should I round?
Only at the final step.
How do I split $100 among three people?
$33.33, $33.33, and $33.34.