Rounding Calculator

How to use the rounding calculator

1. Type the value in Number to round. Type decimals with a point (commas may group thousands, as in 1,234.5); scientific notation such as 1.2e-3 works too.
2. In Round to, choose Decimal places, Significant figures or Nearest multiple of N.
3. Enter the amount in the box below it: the number of decimal places, the number of significant figures, or N itself (5, 0.05, 0.25…).
4. Pick a Rounding rule. The Result updates as you type; Round and Copy are there when you need them.

The table Same rounding with each rule shows what every rule would give, which makes the differences easy to see. The Step by step panel explains the calculation: the rounding increment, how many increments fit in your number, how that count is rounded, and the multiplication back.

The rounding rules

All rules agree on most numbers; they differ on exact halves (2.5, 0.125…) and, for the directed rules, on everything that is not already a multiple of the increment.

• Round half up (away from zero): the rule taught at school. A 5 rounds away from zero: 2.5 → 3, −2.5 → −3. This is also what the ROUND function of spreadsheets does.
• Round half to even (banker’s): a 5 rounds to the nearest even digit: 2.5 → 2, 3.5 → 4, 0.125 → 0.12. Over many values the ups and downs cancel out, so totals are not biased upward. It is the default in IEEE 754 arithmetic and in many programming languages.
• Round down (toward −∞): the floor. 2.9 → 2 and −2.1 → −3.
• Round up (toward +∞): the ceiling. 2.1 → 3 and −2.9 → −2. Useful when you must not come up short, such as buying enough boxes or tiles.
• Toward zero (truncate): simply drops the extra digits. 2.9 → 2 and −2.9 → −2.

Decimal places, significant figures and multiples

Decimal places count digits after the decimal point: 3.14159 to 2 decimal places is 3.14. A negative number of decimal places rounds to the left of the point: −1 rounds to the nearest ten, −2 to the nearest hundred (1234.5 → 1200).

Significant figures count from the first nonzero digit, wherever the decimal point is: 0.00123456 to 3 significant figures is 0.00123, and 123456 is 123000. The tool also writes the result in scientific notation (1.23 × 10⁵), which shows the precision without ambiguous trailing zeros.

Nearest multiple of N handles cash rounding (N = 0.05), quarter hours (N = 0.25), prices ending in 5 or 10, and package sizes. For 1.13 and N = 0.05, the result is 1.15.

Trailing zeros are kept when they are part of the requested precision: 2.5 to 3 decimal places is shown as 2.500.

Exact decimal arithmetic

Many calculators and programming languages round 2.675 to 2.67, because the binary floating-point value closest to 2.675 is actually 2.67499999…. This tool works with exact decimal fractions, so 2.675 rounded half up to two places is 2.68, as expected on paper.