Quick wins for a faster PC:
Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →Repair Windows errors before they cause bigger problemsFix Now →Scan for outdated or missing drivers - takes under a minuteDriver Scan →Gaussian rounding—more commonly called banker’s rounding or round-half-to-even—rounds to the nearest value, except at an exact halfway point, when it chooses the candidate whose last retained digit is even. That is why 1.5 rounds to 2 but 2.5 also rounds to 2: both ties select an even result.
What does round half to even mean?
Rounding has two parts: find the nearest permitted value, then decide what to do if the number is exactly halfway between two choices. Half-even uses the nearest choice for ordinary values and uses parity only to break an exact tie.
| Value | Result at integer precision | Why |
|---|---|---|
| 2.4 | 2 | 2 is nearer than 3; this is not a tie. |
| 2.6 | 3 | 3 is nearer than 2; this is not a tie. |
| 1.5 | 2 | The tie is resolved in favor of even 2. |
| 2.5 | 2 | The tie is resolved in favor of even 2. |
| 3.5 | 4 | The tie is resolved in favor of even 4. |
| 4.5 | 4 | The tie is resolved in favor of even 4. |
So “even” does not mean always round down, nor does it mean round every value to an even number. It means that at a tie, choose the candidate with an even last retained digit. For negative values, the same nearest-even principle applies; NumPy’s documentation, for example, shows −0.5 rounding to 0.
How half-even differs from other rounding rules
Half-even is one tie-breaking policy, not a synonym for ordinary rounding. Under half-up, an exact half is sent upward according to that rule; under half-away-from-zero, it is sent away from zero. Directed modes such as ceiling and floor choose a direction rather than the nearest-even tie candidate. Python’s Decimal arithmetic supports selectable modes including half-even, half-up, half-down, ceiling, and floor; the active context determines the mode for arithmetic operations. See the Python Decimal documentation and PEP 327.
Recommended Free Tools
At one decimal place, 1.25 becomes 1.2 under half-even because the retained digit 2 is even; 1.35 becomes 1.4 because 4 is even. The same rule works at any chosen precision: identify the last digit that will remain, and use its parity only if the discarded portion lands exactly halfway.
How common tools handle rounding
| Tool or feature | Documented behavior | What to watch |
|---|---|---|
Python built-in round |
Exact halfway cases are rounded to the even result. | Float representation can mean a decimal-looking value is not an exact tie. See Python’s round documentation. |
Python decimal |
Provides selectable rounding modes, including half-even. | Check or set the decimal context when a particular rule is required. See the Decimal documentation. |
NumPy round |
Exact halfway values are rounded to the nearest even value. | Its fast floating-point algorithm can be inexact because decimal fractions may not be exactly represented in binary and scaling can add error. See NumPy’s round documentation. |
Excel ROUND |
Microsoft says fractional parts of 0.5 or greater round up. | This describes the ROUND function, not display formatting or every Excel feature. Microsoft’s guidance applies to Microsoft 365, Excel 2024, and Excel 2021. See Microsoft Support’s “Round a number”. |
Why Python or NumPy may surprise you
A decimal fraction such as 16.055 generally cannot be represented exactly as a binary floating-point value. A function therefore receives the stored binary approximation, not necessarily the exact decimal tie a person sees on screen. NumPy also documents a fast rounding method based on scaling by a power of ten; that computation can introduce additional error. Its examples show results that differ from Python’s built-in round.
This does not necessarily mean the tools disagree about the half-even rule. It may mean the value presented to the rule is not an exact halfway value in that tool’s numeric representation, or that the implementation’s computation introduces a small error. NumPy’s documented caveat and examples are at numpy.round.
Rounding a value is not the same as formatting it
A displayed value can have fewer decimal places without changing the number stored underneath. Conversely, a rounding function can produce a new rounded value. Microsoft explicitly distinguishes changing displayed decimal places through formatting from using Excel’s ROUND function to round a number; see Microsoft’s guidance.
When two programs show different decimal output, first check whether one is only formatting the display and the other is changing the value. Then check the chosen precision, numeric representation, and tie rule.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.When to choose banker’s rounding
Half-even sends exact ties in alternating directions depending on the retained digit’s parity, rather than sending every positive tie in one direction. This avoids the directional tendency inherent in always rounding positive ties upward, but the cited official documentation does not quantify an aggregate error reduction or establish that half-even is best for every application.
For reliable cross-tool results, specify four things: the rounding rule, the precision or increment, the numeric representation (such as binary float or decimal), and whether the goal is to alter the value or only its display. If a financial, scientific, or business specification mandates a particular decimal policy, configure that policy explicitly rather than assuming every function named round behaves the same way.
Quick Recap
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
Free tools Windows power users keep installed
One-click scans. No signup required.
