Rounding Calculator

Number & Precision

The main result uses the mode you select; the comparison block always shows all five.

NumberDecimals and negatives are fine

Round to

Decimal places / significant figures

Nearest multiple ofUsed in "nearest multiple" mode — try 5, 10, 0.25

Rounding mode

ROUNDED

—

Difference from the original—

Percentage error introduced—

Digits removed—

Original value—

Every mode, same input

Half up—

Half to even (banker's)—

Half down—

Ceiling—

Floor—

Truncate—

—

The five modes and where each one belongs

Half up sends exact halves away from zero: 2.5 → 3. It is what school teaches and what most people expect.

Half to even, or banker's rounding, sends exact halves to the nearest even number: 2.5 → 2, 3.5 → 4. Half up has a systematic upward bias because every tie goes the same way; over thousands of transactions that accumulates into real money. Sending half the ties down cancels it, which is why it is the IEEE 754 default and the standard in financial systems.

Ceiling and floor always go one direction regardless of the digit — used for pricing tiers, shipping units and anything where you must not undershoot. Truncation simply discards digits, which is floor for positives but ceiling for negatives, and it is the behaviour of an integer cast in most programming languages.

Decimal places versus significant figures

Two decimal places on 0.00043 gives 0.00, destroying the number entirely. Two significant figures gives 0.00043 — the precision is relative to the value rather than to the decimal point. For measured quantities spanning different magnitudes, significant figures are almost always the right choice.

Why rounding twice is dangerous

Round 2.44 to one decimal place and you get 2.4; round that to a whole number and you get 2. Round 2.44 straight to a whole number and you also get 2. But 2.45 → 2.5 → 3 whereas 2.45 → 2 in one step. Chained rounding drifts upward. Always round once, from the original value, at the last possible moment.

Floating point makes this worse than it looks

Computers store 0.1 and 2.675 as the nearest available binary fraction, not exactly. 2.675 is really 2.67499999999999982..., so a correct half-up implementation rounds it to 2.67, not 2.68 — and users file this as a bug every single day. This calculator applies a small epsilon correction so results match hand arithmetic, but it is worth knowing why the discrepancy exists.

Frequently Asked Questions

What is banker's rounding and why use it?

It rounds exact halves to the nearest even number, so ties go up half the time and down half the time. Ordinary half-up rounding always sends ties away from zero, which introduces a small but systematic upward bias across many values — a real problem in accounting.

How do I round to significant figures?

Count from the first non-zero digit rather than from the decimal point. Select the significant-figures mode above and the leading zeros are handled for you.

Why does my spreadsheet round 2.675 to 2.67?

Because 2.675 cannot be stored exactly in binary floating point; the stored value is fractionally below 2.675, so it correctly rounds down. It is a representation issue, not a rounding bug.

What is the difference between floor and truncate?

They agree for positive numbers and disagree for negatives. Floor always goes down, so −2.5 becomes −3. Truncate simply drops the decimal part, so −2.5 becomes −2.

Where these numbers come from

Sources

Official publications only. Links open the original document in a new tab.

National Institute of Standards and Technology Special Publication 811 — Guide for the use of the SI Significant figures and rounding conventions
National Institute of Standards and Technology CODATA fundamental physical constants Values of the fundamental physical constants