Banker's Rounding

Banker's rounding (Round Half Even) resolves exact ties by rounding to the nearest even number.

Use these steps to apply Banker's Rounding correctly:

The Banker's Rounding rule dictates that ties are broken by looking at the parity of the candidate results. When rounding to the nearest value, any discarded portion that is strictly less than 5 rounds to the closer lower-magnitude number. Any discarded portion strictly greater than 5 rounds to the closer higher-magnitude number. When the discarded portion is precisely 5 followed by no other non-zero digits, the result that has an even number as its least significant digit is chosen.

2.5 is exactly halfway between 2 and 3. Banker's Rounding chooses the even result, and 2 is even while 3 is odd. Therefore, 2.5 rounds to 2.

Conversely, 3.5 is exactly halfway between 3 and 4. Since 4 is even and 3 is odd, Banker's Rounding selects 4. Thus, 3.5 → 4. This pattern alternates for every halfway case.

Not every number ending in 5 is an exact halfway case. The even rule only applies to exact halfway values. For example, when rounding to the nearest whole number:

• 2.5 is exactly halfway. The rule applies, and it rounds to 2.
• 2.51 is above halfway. It is closer to 3, so it rounds to 3. The even rule is skipped.
• 2.49 is below halfway. It is closer to 2, so it rounds to 2. The even rule is skipped.

This pattern ensures that half of the tie cases round down (e.g. 2.5 → 2, 4.5 → 4) and the other half round up (e.g. 3.5 → 4, 5.5 → 6), balancing the overall outcomes.

When rounding to a specific decimal place, the exact halfway condition occurs when the next digit is 5 and all subsequent digits are zero. The retained digit determines the tie result.

To 1 Decimal Place

• 2.25 → 2.2
• 2.35 → 2.4
• 2.45 → 2.4
• 2.55 → 2.6

To 2 Decimal Places

• 2.125 → 2.12
• 2.135 → 2.14
• 2.145 → 2.14
• 2.155 → 2.16

It is important to remember that the even rule only applies when the discarded portion is exactly halfway (like .05, .005). If the value was 2.1251, it is above halfway, so it rounds up to 2.13.

The exact same rule applies to negative numbers. Banker's Rounding always selects the even candidate for ties. Parity (even/odd) does not change with the sign.

Round Half Up always pushes exact ties away from zero (upward for positive numbers), while Banker's Rounding pushes ties to the nearest even number.

Banker's Rounding vs Round Half Down

Round Half Down always pushes exact ties toward zero, whereas Banker's Rounding depends on the even-number rule.

Banker's Rounding vs Traditional Rounding

In many elementary math contexts, the familiar rounding rule is Round Half Up, where an exact halfway value is rounded upward. Banker's Rounding uses a different tie-breaking rule.

Banker's Rounding vs Round to Even

Banker's Rounding and Round Half Even are the exact same rounding method. They are different names for identical logical operations.

When repeated calculations contain many exact halfway values, always rounding ties in one direction (like Half Up does) can create systematic bias. Round Half Even sends some ties upward and some ties downward based on parity. This can reduce rounding bias over large collections of calculations.

Consider the task of summing a dataset containing several exact halfway values. By comparing the results of Half Up and Half Even against the exact mathematical sum, the bias-reducing effect becomes clear:

The exact sum is 12.0. Half Up introduces a +2 bias because every tie was rounded upward. Half Even produces no net rounding error in this particular example because the upward and downward tie adjustments balance each other. This does not mean Half Even always produces an exact total.

Banker's Rounding is used in some financial, accounting, statistical, scientific, and software systems. The actual rounding rule depends on the applicable standard, software, or organization.

Different languages and libraries implement different rounding rules. Never assume that a function named round() defaults to a specific method. Check the documentation or explicitly request the desired rounding mode.

Does Python Use Banker's Rounding?

Yes. Python's built-in round() function uses Banker's Rounding (Round Half Even) by default for tie cases. For example, round(2.5) evaluates to 2, and round(3.5) evaluates to 4. Note that due to binary floating-point representation, some decimal fractions might not be stored as exact halfway values, which can occasionally bypass the tie rule.

C# / .NET

In C# and .NET, `Math.Round()` defaults to Banker's Rounding (MidpointRounding.ToEven). You can change this behavior by explicitly passing `MidpointRounding.AwayFromZero`.

Java

Java's `Math.round()` uses Round Half Up. To use Banker's Rounding, you must use the `BigDecimal` class and explicitly specify `RoundingMode.HALF_EVEN`.

JavaScript

JavaScript's `Math.round()` uses Round Half Up (specifically, toward positive infinity). JavaScript does not have a built-in Banker's Rounding function, so you must implement a custom rounding algorithm.

Does Excel Use Banker's Rounding?

No. Excel's standard ROUND function uses Round Half Up. To perform Banker's Rounding in Excel, you must either write a custom VBA function or use a more complex array formula to evaluate parity.

Conceptually, the Banker's Rounding rule states: evaluate the distance from the original number to the two closest allowed values. If one distance is shorter, select that value. If the distances are identical (an exact halfway case), compare the two possible rounded results and choose the one whose retained digit is even (divisible by 2).

Test your understanding with these practice questions.