Round to Even Calculator

1. 1. Enter a number.
2. 2. Select the rounding precision.
3. 3. The calculator identifies the nearest possible results.
4. 4. It determines whether the number is below, above, or exactly at the midpoint.
5. 5. At an exact midpoint, the calculator chooses the result whose retained digit is even.
6. 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. 1. Scale the number to the desired precision.
2. 2. Identify the two nearest candidate results.
3. 3. Determine whether the value is below, above, or exactly halfway.
4. 4. At an exact midpoint, select the candidate whose retained digit is even.
5. 5. Scale back to the original precision.

Many programming languages use round-to-even as their default rounding method.

• Python: Python 3's built-in round() function uses round ties to even as its default behavior for numeric types.
• C#: Uses MidpointRounding.ToEven by default for Math.Round().
• Java: Available via RoundingMode.HALF_EVEN.
• JavaScript: Math.round() uses half up toward positive infinity. It does not implement general-purpose banker's rounding.

This can occasionally cause numbers that look like exact midpoints to not trigger the midpoint rule.

roundTiesToEven is the default rounding-direction attribute defined by the IEEE 754 standard for binary floating-point arithmetic.

Because computers use binary floating-point representation, some decimal fractions cannot be represented exactly.

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

This can occasionally cause numbers that look like exact midpoints to not trigger the midpoint rule.

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

• - When summing large datasets of rounded numbers.
• - When you need to minimize systematic rounding error.
• - When financial regulations or accounting principles require it.
• - When complying with the IEEE 754 floating-point standard.
• - When default programming language behaviors already apply it.

• - Assuming round to even always rounds down. (It rounds up if the higher digit is even).
• - Thinking it only applies to whole numbers. (It applies to decimals and significant figures).
• - Confusing it with floor or truncation.
• - Forgetting that non-midpoint values still round to the nearest value normally.

What is round to even?

Round to even is a rule that rounds exact midpoint numbers to the nearest even value to prevent systematic bias.

What is 2.5 rounded to even?

2.5 rounded to even is 2. It is halfway between 2 and 3, and 2 is even.

What is 3.5 rounded to even?

3.5 rounded to even is 4. It is halfway between 3 and 4, and 4 is even.

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

Yes, round-to-even and Banker's Rounding refer to the exact same method.

Does round-to-even always round down?

No, it rounds to whichever adjacent number is even. It rounds 2.5 down to 2, but rounds 3.5 up to 4.