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.

Binary floating point cannot store many decimal fractions exactly, so the result can depend on the value and intermediate arithmetic. In current JavaScript, 3.145 times 100 is 314.5 and Math.round gives 3.15. A value such as 1.005 can land just below its decimal halfway point and round down unexpectedly. This calculator detects near-ties with a small tolerance, so 3.145 rounds to 3.15 with half-up.

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.