Round any number to decimal places or the nearest 10, 100 or 1,000, and see how bankers rounding works next to the usual school method. Five methods are available: standard, banker’s, ceiling, floor and truncate.
Choose how precise you want the result and which rounding method to use. “Round half up” is the everyday default; “banker’s rounding” rounds halves to the nearest even digit.
Rounding replaces a number with a simpler nearby value at the chosen precision. The method matters only when the digit is exactly halfway (a 5).
How Does Bankers Rounding Work?
Banker’s rounding sends a value that sits exactly halfway to the nearest even number. So 2.5 rounds to 2, 3.5 rounds to 4 and 4.5 rounds to 4. Numbers that are not exactly halfway round as usual. Over many values, the ups and downs cancel out instead of all drifting upward.
| Number | Half up (standard) | Half to even (banker’s) |
|---|---|---|
| 0.5 | 1 | 0 |
| 1.5 | 2 | 2 |
| 2.5 | 3 | 2 |
| 3.5 | 4 | 4 |
| 4.5 | 5 | 4 |
- Check the value is exactly halfway: 2.5 is.
- Find the two neighbors: 2 and 3.
- Pick the even one: 2.
The Formula Behind Each Method
Every method scales the number, rounds it, then scales it back.
Formula: Scale the number by the chosen place value, factor = 10^p (where p is the number of decimal places, or negative for nearest 10/100/1,000), then apply the rounding method to x × factor, then divide back by factor. Round half up rounds a halfway value away from zero (2.5 → 3). Round half to even (banker’s rounding) rounds a halfway value to whichever neighbor is even (2.5 → 2, but 3.5 → 4). Ceiling always rounds toward positive infinity, floor always rounds toward negative infinity, and truncate simply drops the digits past the chosen place without rounding at all.
- Number: the value you want to round
- Round to: the precision, from the nearest whole number and 1-4 decimal places to the nearest 10/100/1,000. To round to the nearest hundred, 3,847 becomes 3,800.
- Rounding method: how halfway cases are resolved: half up, half to even (banker’s), ceiling, floor, or truncate
Example Scenarios
| Number | Round To | Method | Result |
|---|---|---|---|
| 3.14159 | 2 decimal places | Half up (standard) | 3.14 |
| 2.5 | Nearest whole number | Half up (standard) | 3 |
| 2.5 | Nearest whole number | Half to even (banker’s) | 2 |
| 3.5 | Nearest whole number | Half to even (banker’s) | 4 |
| -3.7 | Nearest whole number | Ceiling (always up) | -3 |
| -3.7 | Nearest whole number | Floor (always down) | -4 |
Does 5 Round Up or Down? It Depends on the Method
Under the school method a 5 rounds up; under banker’s rounding it goes to the even side.
- Standard (round half up): 2.5 becomes 3. This is the school method.
- Banker’s rounding (round half to even): 2.5 becomes 2 and 3.5 becomes 4. It avoids upward bias across many values, which suits accounting and large datasets.
- Ceiling and floor always go up or down, useful for whole units or hard limits.
- Truncate vs round down: truncate simply drops digits, so 7.89 becomes 7.8 at one decimal place. For positive numbers that matches floor; for negatives it does not.
Round only once, at the end, since rounding intermediate steps can drift from the true answer. When you round negative numbers, watch the direction: the floor of -2.3 is -3, not -2. If results must match a spreadsheet, check which rule that software applies. The Wikipedia article on rounding compares these rules in depth, and each mode in this calculator maps to one of them.
Common questions about rounding
How does banker’s rounding work?
When a number sits exactly halfway, banker’s rounding (round half to even) picks whichever neighbor is even. So 2.5 rounds to 2 and 3.5 rounds to 4. Anything not exactly halfway rounds normally.Does 5 round up or down?
Under the standard school rule, a 5 rounds up, so 2.5 becomes 3. Under banker’s rounding it goes to the even neighbor, so 2.5 becomes 2. Which is right depends on the convention your class, field or software uses.How do you round negative numbers?
Standard rounding treats a negative number like its positive twin and moves halfway values away from zero, so -2.5 becomes -3. Ceiling and floor differ: ceiling moves toward positive infinity (-3.7 becomes -3) and floor toward negative infinity (-3.7 becomes -4).What’s the difference between truncate and round down?
Truncating deletes the digits past the chosen place, which for positive numbers looks the same as rounding down (floor). With negatives they split: floor(-3.7) is -4, but truncating -3.7 gives -3, since truncation always moves toward zero.How do I round a number to the nearest 100 or 1,000?
Choose “Nearest 100” or “Nearest 1,000” from the Round To list. The calculator scales the number down by 100 or 1,000, rounds it, and scales it back up, so 3,847 becomes 3,800 to the nearest hundred.When should I use ceiling or floor instead of standard rounding?
Use ceiling when you always need to round up, for example working out how many boxes are needed for a quantity. Use floor when you always need to round down, such as counting how many complete units fit into a total.Related Calculators
Choosing how to round often ties into choosing how much precision to keep in the first place. The significant figures calculator and the scientific notation converter both help with that, while the exponent calculator is handy when the numbers you’re rounding come from a power calculation.