Enter one number and see it rounded to every common place at once — nearest million down to nearest thousandth — with standard (half up) and banker's (half even) rounding side by side, so you can see exactly where the two rules disagree.
1,234.5 rounded to the whole number (standard rounding)
1,235
Rounded to every place — click a row to select it
Round to
Standard (half up)
Banker’s (half even)
Nearest million
0
0
Nearest hundred thousand
0
0
Nearest ten thousand
0
0
Nearest thousand
1,000
1,000
Nearest hundred
1,200
1,200
Nearest ten
1,230
1,230
Whole number
1,235
1,234
Nearest tenth (0.1)
1,234.5
1,234.5
Nearest hundredth (0.01)
1,234.50
1,234.50
Nearest thousandth (0.001)
1,234.500
1,234.500
Amber values mark places where standard and banker’s rounding disagree — your number sits exactly halfway at those places.
📌 Standard rounding sends an exact .5 away from zero (2.5 → 3). Banker’s rounding sends it to the nearest even digit (2.5 → 2, 3.5 → 4), which cancels out bias over many roundings — it is the default in Python, IEEE 754 floating point, and much accounting software.
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How rounding works
To round to a place, look at the single digit immediately to its right. If that digit is less than 5, keep the place digit as it is (round down); if it is 5 or more, add one to the place digit (round up). Then replace everything to the right with zeros — or drop it, for decimal places.
Worked example: round 1,234.5 to each place. To the nearest thousand, the hundreds digit is 2, so it rounds down to 1,000. To the nearest hundred, the tens digit is 3 — down to 1,200. To the nearest ten, the ones digit is 4 — down to 1,230. To the nearest whole number, the tenths digit is exactly 5 — standard rounding goes up to 1,235, but banker's rounding goes to the nearest even number, 1,234. That last row is the only place the two rules ever disagree: an exact half.
Half up vs banker's rounding: the 2.5 problem
School rounding says "5 rounds up", so 2.5 → 3 and 3.5 → 4. Notice the asymmetry: of the ten possible final digits, 1–4 round down (four cases) but 5–9 round up (five cases). Sum millions of rounded values — interest payments, tax lines, lab measurements — and that extra half-case pushes the total systematically high. Banker's rounding fixes it by sending exact halves to the nearest even digit: 2.5 → 2, 3.5 → 4, 4.5 → 4, 5.5 → 6. Halves now round down as often as up, and the bias cancels. Everything that is not an exact half behaves identically in both systems.
Rounding vs truncating: truncating just cuts digits off (3.999 → 3), always moving toward zero with an error of up to a whole unit. Rounding picks the closest value (3.999 → 4) and is never off by more than half a unit — which is why "round" and "truncate" give different answers for almost every number.
Frequently asked questions
Look at the thousandths digit (the third decimal). If it is 5 or more, add one to the hundredths digit; otherwise drop everything after the second decimal. For example 3.14159 → 3.14 (the third decimal is 1, so round down) and 2.678 → 2.68 (the 8 rounds the 7 up). The calculator shows this row — and every other place — instantly.
Banker’s rounding (round half to even) sends an exact half to the nearest even digit instead of always up: 2.5 → 2 but 3.5 → 4. Over many roundings the ups and downs cancel, removing the small upward bias of always rounding halves up. It is the default in Python 3, IEEE 754 floating-point arithmetic, and much financial software.
It depends on the rule. Standard school rounding (half up, away from zero) rounds 0.5 up to 1 and -0.5 down to -1. Banker’s rounding rounds 0.5 to 0, because 0 is the nearest even number. Both are correct — they are simply different conventions, which is why this calculator shows both side by side.
US consumer prices round half up to the nearest cent: $4.955 becomes $4.96. Accounting and financial systems often prefer banker’s rounding to avoid systematic bias when summing thousands of rounded amounts — a fraction of a cent of bias per transaction adds up. For sales tax, most US states round the computed tax half up to the cent.
Truncating simply cuts digits off without looking at them: 3.999 truncated to a whole number is 3. Rounding picks the closest value at the chosen place: 3.999 rounds to 4. Truncation always moves toward zero and can be off by almost a full unit, while rounding is off by at most half a unit.