What This Calculator Does
Rounding replaces a number with a shorter, simpler value that is close to the original. This tool rounds any number to between 0 and 10 decimal places using one of six rounding methods, and explains each result step by step.
Unlike a quick ROUND() in a spreadsheet, it rounds the digits you actually typed — so it
never trips over floating-point quirks like 12.345 becoming 12.34.
How to Use It
- Type the number you want to round.
- Choose how many decimal places to keep (
0means round to a whole number). - Pick a rounding method. The result and explanation update instantly.
The Six Rounding Methods
| Method | What it does | 2.5 → 0 dp | −2.5 → 0 dp | 2.1 → 0 dp |
|---|---|---|---|---|
| Round half up | Nearest; ties go away from zero | 3 | −3 | 2 |
| Round half down | Nearest; ties go toward zero | 2 | −2 | 2 |
| Round half to even | Nearest; ties go to the even digit | 2 | −2 | 2 |
| Round up (ceiling) | Always toward +∞ | 3 | −2 | 3 |
| Round down (floor) | Always toward −∞ | 2 | −3 | 2 |
| Round toward zero | Drops the extra digits | 2 | −2 | 2 |
Round half up (the everyday default)
The method most people learn in school: if the first dropped digit is 5 or more, round up. An exact half (like 2.5) rounds away from zero, so 2.5 → 3 and −2.5 → −3.
Round half down
Identical to half up, except an exact half rounds toward zero: 2.5 → 2, −2.5 → −2.
Round half to even (banker’s rounding)
Rounds an exact half to the nearest even digit: 2.5 → 2, but 3.5 → 4. Because halves go up half the time and down half the time, a long column of rounded numbers keeps its total closer to the true sum. This is the default in accounting software and the IEEE 754 floating-point standard.
Ceiling and floor
Ceiling always moves toward positive infinity; floor always moves toward negative infinity. They only differ from the “half” methods when there is anything to drop at all — 2.1 ceilings to 3, while 2.9 floors to 2.
Round toward zero (truncate)
The simplest method: just chop off the extra digits. 2.9 → 2 and −2.9 → −2.
Why ROUND() and toFixed() Sometimes Look Wrong
Computers store decimals in binary. Many everyday decimals have no exact binary form, so a value like 12.345 is actually stored as 12.34499999999999…. A rounding routine that works on that stored value sees a 4 in the next place and rounds down to 12.34 — not the 12.35 you expected.
This calculator avoids the problem by rounding the decimal digits you typed, not the binary approximation. So 12.345 → 12.35, 1.005 → 1.01, and 2.675 → 2.68, every time.
Rounding Negative Numbers
The “half” methods describe ties relative to zero, so −2.5 with half up goes to −3 (away from zero). Ceiling and floor instead follow the number line: ceiling moves −2.1 up to −2, while floor moves −2.1 down to −3.