Rounding Calculator
Decimal Places & Rounding Modes
Rounding Rules, Explained
Not every rounding method behaves the same way at the boundary case — a value exactly halfway between two numbers. Choosing the right mode matters for financial reporting, scientific data, and everyday estimates alike.
Half Up, Half Down, Ceiling, Floor, and Half to Even each treat the tie-breaking case differently — try 2.5 in every mode to see the results diverge.
A positive precision rounds to decimal places (2.345 → 2.35 at precision 2). A negative precision rounds up the number line, to the nearest ten, hundred, or thousand.
Half to Even (Banker's Rounding)
Instead of always breaking ties the same direction, half-to-even rounding sends a tied value to whichever neighboring number is even: 2.5 → 2, but 3.5 → 4. Across a large dataset, this cancels out rounding bias in both directions, which is why it's the IEEE 754 default and common in accounting systems.
Key Takeaways
- Ceiling and floor ignore the 0.5 boundary entirely. They round toward positive or negative infinity respectively, no matter how close the value already is.
- Negative precision rounds "up" the place-value scale. Use -1, -2, or -3 for the nearest ten, hundred, or thousand.
- Half to even reduces cumulative rounding bias when applied across many values, which is why financial systems often prefer it.
Frequently Asked Questions
- Enter the number you want to round.
- Choose a precision preset, or type a custom precision (positive for decimal places, negative for nearest ten/hundred/thousand).
- Choose a rounding mode.
- Click "Calculate" to see the rounded result.
Half Up rounds a value exactly halfway between two numbers away from zero (2.5 → 3, -2.5 → -3). Half Down rounds a halfway value toward zero (2.5 → 2). Ceiling always rounds up to the next value, regardless of how close it already is (2.1 → 3). Floor always rounds down (2.9 → 2). Half to Even ("banker's rounding") rounds a halfway value to whichever neighbor is even (2.5 → 2, 3.5 → 4), which reduces cumulative bias when rounding many numbers.
Use a negative precision. A precision of -1 rounds to the nearest 10, -2 rounds to the nearest 100, and -3 rounds to the nearest 1,000. A precision of 0 rounds to the nearest whole number, and positive precisions (1, 2, 3…) round to that many decimal places.
If you always round exact halfway values up, repeatedly rounding a large dataset introduces a small upward bias over many calculations. Half-to-even rounding alternates which direction ties go, which keeps the average rounding error closer to zero — this is why it's the default rounding rule in many financial and statistical systems, including IEEE 754 floating-point arithmetic.
Precision represents a whole number of decimal places (or powers of ten to round to), so it must be an integer. A value like 2.5 doesn't correspond to any real rounding position, so the calculator rejects it with a clear error instead of guessing what you meant.