Rounding Calculator

Rounding reduces a number to a simpler form while controlling how much precision you keep. Every rounding rule answers the same question — which digit to keep and whether to increase it — but different conventions break ties differently. Financial reporting, scientific publishing, engineering tolerances, and classroom homework each expect specific rules, so comparing methods side by side prevents silent mistakes when 3.145 becomes either 3.14 or 3.15 depending on context.

Rounding to decimal places counts digits after the decimal point. To round 3.145 to two decimals, inspect the third decimal digit (5). In round half up — the rule most students learn first — a third digit of 5 or greater bumps the second digit up, giving 3.15. Round half even (banker's rounding) breaks ties on an even last digit: 3.145 has an odd second digit (4), so half even also rounds up to 3.15, but 3.135 would stay 3.14 because 3 is odd and the tie favors the even neighbor. Half even reduces bias when you round thousands of ledger entries.

Significant figures count meaningful digits from the first non-zero digit through the last reported digit. Rounding 0.004567 to two significant figures yields 0.0046 because the leading zeros are placeholders, not significant. Scientific measurements should match instrument precision: a ruler marked to millimeters should not report micrometers after rounding. Use sig fig rules alongside the scientific notation converter when presenting very large or small quantities compactly.

Ceiling and floor are not rounding in the usual sense but bound a value. ceil(3.2) = 4 because the ceiling function returns the smallest integer greater than or equal to x. floor(3.8) = 3 returns the greatest integer less than or equal to x. These appear in discrete math, inventory planning (how many boxes to order), and programming. Nearest integer (standard round) maps 3.5 to 4 and 4.5 to 5 under half-up integer rounding.

Floating-point arithmetic on computers can produce values like 2.6750000000000004 instead of exact 2.675, which is why this calculator uses careful digit-by-digit logic for decimal places rather than naive multiplication by powers of ten. For money, always round at the end of a calculation chain, not after every intermediate step, unless regulations say otherwise. Pair this tool with the percentage calculator when discount and tax lines must display two decimal cents, and with the fraction calculator when exact rational values precede decimal rounding.

Select your value, choose decimal places or significant figures, and review all methods in one view. Document which convention your course or industry requires — chemistry labs often specify sig figs, banking uses half even, and everyday math homework typically uses half up. Copy the appropriate rounded result directly into reports, spreadsheets, or exam answers with confidence about which rule was applied.