Rounding Calculator

Half-up is the standard school rule: any value ending in exactly .5 rounds up, so 2.5 becomes 3 and 3.5 becomes 4. Half-even, also called banker's rounding, sends ties to the nearest even digit instead. That turns 2.5 into 2 and 3.5 into 4. Half-even is preferred in accounting, statistics, and IEEE 754 floating-point math because it removes the upward bias you get from always rounding .5 up across a long list of numbers.

Because 3.145 cannot be stored exactly as a binary float. Internally it is closer to 3.1449999999999996, so a naive Math.round call sees it as below the halfway point and rounds down. This calculator corrects for that by detecting ties with a small tolerance, so 3.145 rounds to 3.15 with half-up, the way you would expect on paper.

Decimal places count digits after the decimal point: 0.004567 to 2 decimal places is 0.00. Significant figures count meaningful digits from the first non-zero digit: 0.004567 to 2 significant figures is 0.0046. Use sig figs when the scale of the number can vary a lot, like in scientific measurements, and decimal places when you need a fixed number of digits after the point, like in currency.

Ceiling always rounds toward positive infinity: 3.2 becomes 4, and -3.7 becomes -3. Floor always rounds toward negative infinity: 3.7 becomes 3, and -3.2 becomes -4. Truncate always rounds toward zero by dropping the fractional part: 3.7 becomes 3, and -3.7 becomes -3. None of these care whether the fraction is above or below 0.5; they only care about direction.

A negative place value rounds to a digit after the decimal point. Place value 0 rounds to the nearest whole number, 1 to the nearest ten, 2 to the nearest hundred. Going the other way, -1 rounds to the nearest tenth (0.1), -2 to the nearest hundredth (0.01), and -3 to the nearest thousandth (0.001). So 12345 at place value 2 becomes 12300, and 12.3456 at place value -2 becomes 12.35.