Round to Even Calculator

When the value is exactly halfway between two integers, round half to even selects the even integer.

1. Enter a number.
2. Select the rounding precision.
3. The calculator identifies the nearest possible results.
4. It determines whether the number is below, above, or exactly at the midpoint.
5. At an exact midpoint, the calculator chooses the result whose retained digit is even.
6. It displays the rounded result.

Round to even, also called round half to even, rounds a number to the nearest value. When a number falls exactly halfway between two possible results, the method chooses the even result.

Round half to even behaves differently depending on where the value falls relative to the midpoint:

• Below the midpoint: Rounds to the lower value (e.g., 2.4 → 2).
• Above the midpoint: Rounds to the higher value (e.g., 2.6 → 3).
• Exactly at the midpoint: Rounds to the even value.

The midpoint rule is the central concept. For example, 3.4 rounds to 3, and 3.6 rounds to 4, but exactly 3.5 rounds to 4.

A halfway value, or tie value, is a number that is exactly equidistant from two possible rounded results.

• 2.5 is exactly halfway between 2 and 3.
• 1.25 is exactly halfway between 1.2 and 1.3.
• 12.125 is exactly halfway between 12.12 and 12.13.

Round half to even needs a specific rule for these exact midpoint cases to determine which way the tie breaks.

At an exact midpoint, look at the two possible rounded results and choose the one whose retained digit is even. The retained digit is the digit at the selected rounding position.

2.5 is exactly halfway between 2 and 3.

• 2 ← 2.5 → 3
• 2 = even
• 3 = odd
• Result = 2

Therefore, round half to even selects 2.

3.5 is exactly halfway between 3 and 4.

• 3 ← 3.5 → 4
• 3 = odd
• 4 = even
• Result = 4

Therefore, round half to even selects 4.

The even or odd test applies to the retained digit at the selected rounding position.

• 1 decimal place: 1.25 → 1.2 (because 2 is the even retained digit). 1.35 → 1.4 (because 4 is the even retained digit). 1.45 → 1.4. 1.55 → 1.6.
• 2 decimal places: 12.125 → 12.12. 12.135 → 12.14.
• 3 decimal places: 7.1125 → 7.112. 7.1135 → 7.114.

Significant figures dictate the overall precision of a number starting from its first non-zero digit. When applying round-to-even to a specified number of significant figures, the rule operates exactly the same way on the final retained digit.

• Rounding 1.25 to 2 significant figures gives 1.2 (because 1.25 is halfway between 1.2 and 1.3, and 2 is even).
• Rounding 1.35 to 2 significant figures gives 1.4 (because 4 is even).
• Rounding 12,500 to 2 significant figures gives 12,000 (because it is halfway between 12,000 and 13,000, and 2 is even).

The rule is based on the parity of the candidate results, not on whether the input is positive or negative.

• -2.5 → -2 (because -2 is even)
• -3.5 → -4 (because -4 is even)
• -4.5 → -4 (because -4 is even)

Do not confuse round-to-even with floor, ceiling, or truncation.

Terminology such as "standard rounding" can vary, but it usually refers to "half up" rounding taught in schools. When a number is not exactly halfway, both methods behave identically.

The difference between these three methods is entirely how they treat exact midpoint ties like 2.5 and 3.5.

Round half to even is commonly known as Banker's Rounding. These are two names for the exact same rule. You may also see it called ties to even or nearest even rounding.

Apply round half to even to handle exact midpoint values and reduce systematic rounding bias across repeated calculations. If every tie is rounded in the same direction, it can create a directional bias. Half-to-even distributes exact midpoint ties between lower and upper results based on parity.

Consider summing these numbers: 2.5, 3.5, 4.5, 5.5.

• Original total: 2.5 + 3.5 + 4.5 + 5.5 = 16
• Half up total: 3 + 4 + 5 + 6 = 18
• Half even total: 2 + 4 + 4 + 6 = 16

This example illustrates the effect of the tie-breaking rule. It does not mean every dataset will produce an identical total.

1. Scale the number to the desired precision.
2. Identify the two nearest candidate results.
3. Determine whether the value is below, above, or exactly halfway.
4. At an exact midpoint, select the candidate whose retained digit is even.
5. Scale back to the original precision.

Different languages and APIs can use different rounding rules.

• Python: Python's built-in round() uses ties-to-even behavior for midpoint cases.
• C#: C# provides MidpointRounding.ToEven.
• Java: Java has multiple rounding APIs and modes (e.g. RoundingMode.HALF_EVEN).
• JavaScript: Math.round() does not implement general-purpose banker's rounding.

Do not assume every programming language uses round-to-even by default.

IEEE 754 defines roundTiesToEven as a supported rounding-direction attribute. This is one reason users encounter round-to-even in numerical computing and programming. Do not assume every programming operation automatically uses this mode.

Computers commonly represent decimal numbers using binary floating-point. Some decimal fractions cannot be represented exactly, which can cause surprising results during calculations.

For example, 0.1 + 0.2 may appear as 0.30000000000000004 in some programming environments.

You must clearly distinguish between the mathematical round-half-to-even rule and the representation of the input value in computer memory.

Round half to even can be used or is supported by many fields, including:

• Numerical computing
• Scientific computing
• Statistics
• Data processing
• Computer arithmetic
• Engineering calculations
• Financial software
• Accounting software
• Programming libraries

It can be useful when:

• Many midpoint values are rounded.
• Reducing systematic midpoint bias is desirable.
• A mathematical or software standard specifies ties-to-even.
• A programming API requires round-half-to-even behavior.

Always follow the rounding rule required by the relevant application, standard, or system.

• Assuming every .5 rounds up.
• Assuming every .5 rounds down.
• Checking the wrong digit.
• Confusing the retained digit with the next digit.
• Confusing round-to-even with floor.
• Confusing round-to-even with ceiling.
• Confusing round-to-even with truncation.
• Assuming all programming languages use the same default.
• Ignoring floating-point representation.
• Using approximate floating-point values when testing exact midpoint behavior.

What is round to even?

Round to even rounds a number to the nearest result and sends exact midpoint ties to the even result.

What is 2.5 rounded to even?

2.5 rounds to 2 because 2 is even and 3 is odd.

What is 3.5 rounded to even?

3.5 rounds to 4 because 4 is even.

Is round-to-even the same as Banker's Rounding?

Yes. Round half to even is commonly called Banker's Rounding.

Does round-to-even always round down?

No. Non-midpoint values round to the nearest result, and midpoint values can round either up or down depending on which candidate is even.