Rounding Calculator

Rounding replaces a number with a nearby, simpler one that is easier to read, say or work with. Type the number, pick the place you want to keep, and choose a rule for numbers that fall exactly halfway. The settings let you type any precision level instead: 2 keeps two decimal places, 0 rounds to a whole number, and negative values such as −3 round to the nearest thousand. Arithmetic is done on the exact decimal digits you enter, so 2.675 rounds to 2.68, not the 2.67 that some software produces because of binary floating point.

Rounding Methods

Rounding has two steps. First identify the digit in the place you are keeping, then look at what comes after it. If the rest is less than half a unit, round down; if it is more than half, round up. The methods differ only in how they handle an exact half, and in whether they always move in one direction.

Round half up sends a tie toward positive infinity: 2.5 becomes 3 and −2.5 becomes −2. Round half down does the opposite, sending ties toward negative infinity, so 2.5 becomes 2 and −2.5 becomes −3. These are simple, but on numbers with mixed signs they shift results in one direction.

Round half away from zero, the rule most people learn in school, moves a tie to the larger magnitude: 2.5 becomes 3 and −2.5 becomes −3. It is symmetric for positive and negative values and is the default in this calculator. Round half towards zero does the reverse: 2.5 becomes 2 and −2.5 becomes −2.

Round half to even, also called banker's rounding or Gaussian rounding, sends a tie to whichever neighbor has an even last digit: 2.5 becomes 2, 3.5 becomes 4 and 0.125 becomes 0.12 at two places. Over many values, half of the ties go up and half go down, so sums and averages are not pushed in either direction. It is the default rounding mode of the IEEE 754 floating-point standard and is common in finance and science. Round half to odd is the mirror image and is used less often.

Ceiling and floor ignore the halfway question entirely. The ceiling always rounds up toward positive infinity, so 2.1 becomes 3 and −2.9 becomes −2; the floor always rounds down, so 2.9 becomes 2 and −2.1 becomes −3. Ceilings are handy for counting things that must be whole, such as how many buses are needed for 130 riders when each holds 50. Truncation, which simply drops the extra digits, matches the floor for positive numbers and the ceiling for negative ones.

Rounding to fractions

Measurements in inches are often rounded to a fraction instead of a decimal place. To round to the nearest 1/n, multiply the number by n, round to a whole number using the chosen method, then divide by n again and reduce the fraction. For 3.2817 inches to the nearest 1/16, 3.2817 × 16 = 52.507, which rounds to 53, giving 53/16 = 3 5/16 inches.

Frequently asked questions