Rounding Calculator

Banker's rounding (half to even) rounds to the nearest even number when the digit is exactly 5. For example, 2.5 rounds to 2 and 3.5 rounds to 4. It is used in finance, accounting, and statistics because it eliminates the upward bias of standard rounding across large datasets. IEEE 754 floating-point arithmetic uses this method by default.

Significant figures count all meaningful digits starting from the first non-zero digit, regardless of the decimal point. Decimal places count only digits after the decimal. For 0.00456: there are 3 significant figures (4, 5, 6) but 5 decimal places. For 1200: there are 2 to 4 significant figures depending on context, but 0 decimal places.

Select the "Nearest 10, 100, 1000" mode and enter the value. To round 12,345 to the nearest 100: the hundreds digit is 3, the next digit is 4 (less than 5), so round down to 12,300. To round 12,367 to the nearest 100: the next digit is 6 (5 or more), so round up to 12,400.

Ceiling (round up) always moves toward positive infinity: 3.2 becomes 4, and -3.8 becomes -3. Floor (round down) always moves toward negative infinity: 3.8 becomes 3, and -3.2 becomes -4. Standard rounding looks at the next digit to decide, while ceiling and floor ignore it entirely.

Measurements have limited precision. Reporting 3.14159 when your instrument only measures to 0.01 implies false accuracy. Rounding to the correct number of significant figures communicates the actual reliability of the data. In engineering, over-rounding can introduce errors that compound across calculations.

Standard rounding works the same way: -2.5 rounds to -3 (away from zero) in half-up mode. In ceiling mode, -2.5 rounds to -2 (toward positive infinity). In floor mode, -2.5 rounds to -3 (toward negative infinity). In Banker's mode, -2.5 rounds to -2 (nearest even).

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