Rounding Calculator

How rounding works

To round to a place, find the digit in that place and look at the digit to its right:

• 5 or more — add 1 to the digit you keep;
• 4 or less — keep it as it is;
• then drop every digit after the place (or replace them with zeros to the left of the point).

3266.528 to the nearest hundredth: the hundredths digit is 2 and the next digit is 8, so the 2 becomes 3 — 3,266.53. 1,234,567 to the nearest thousand: the thousands digit is 4 and the next digit is 5, so it becomes 1,235,000. A carry can ripple: 9.996 to the nearest hundredth is 10.00. The calculator explains which digit decided, and shows the number rounded at every place from millions to millionths.

Tie rules: what happens with an exact 5

Only an exact half — a 5 with nothing after it — is a tie; 2.51 is above half and always rounds up. For ties, several rules are in use:

Half away from zero is the rule taught in school and used by most calculators. Half to even, also called banker’s rounding, is the default in IEEE 754 computer arithmetic and in statistics, and it is NIST’s rule for rounding measured values. JavaScript’s Math.round rounds half up, toward +∞, which is why it turns −2.5 into −2. The other three are rarely used.

Half to even avoids a bias: if every tie rounded up, a long list of prices or measurements would drift upward. The directed rules — up (ceiling), down (floor), toward zero (truncate) and away from zero — ignore the half altogether: ceiling sends 2.1 to 3, which is what you want when buying whole boxes or booking whole hours.

Significant figures

Significant figures count from the first non-zero digit, so the number of decimal places depends on the size of the number. 0.0012345 to three significant figures is 0.00123; 123,456 to two is 120,000; 3.14159 to four is 3.142. Leading zeros are never significant; zeros at the end of a whole number are ambiguous, which is why scientists write 1.2 × 10⁵ for two significant figures. For powers of ten and scientific notation, use the scientific calculator.

Rounding to fractions of an inch

Tape measures mark halves, quarters, eighths and sixteenths. To round 3.14159 inches to the nearest 1/16, multiply the decimal part by 16 (0.14159 × 16 = 2.27), round to 2, and reduce: 2/16 = 1/8, so the answer is 3 1/8 in. The calculator reduces the fraction for you and shows its decimal value. For the reverse — a decimal measurement written as a fraction with every precision at once — see the decimal to fraction calculator.

Why computers sometimes round “wrong”

Most software stores numbers in binary, and many decimals have no exact binary form: 2.675 is stored as 2.674999999999999822… — slightly less than 2.675. Rounded to two places, it becomes 2.67 in JavaScript and Python, although the decimal 2.675 should give 2.68. This calculator does the arithmetic on the decimal digits you type, so it rounds exactly as you would on paper. For money in a spreadsheet, round once at the end rather than at every step; for percentages of a total, the percentage calculator keeps the full precision until the answer.