Rounding and significant figures calculator

How to round a number

Find the last digit you are keeping and look at the digit after it: 5 or more rounds the kept digit up, and 4 or less leaves it unchanged. Rounding 7.3482 to two decimal places gives 7.35, because the next digit is 8. An exact tie, such as 2.345 to two places, depends on the rounding rule.

Decimal places vs significant figures

Decimal places count digits after the decimal point. Significant figures count from the first nonzero digit, so leading zeros never count. 0.0012345 is 0.001 to three decimal places but 0.00123 to three significant figures.

To round to tens, hundreds or thousands, use −1, −2 or −3 decimal places. 4,567 to the nearest hundred (−2 places) is 4,600.

Zeros at the end of a decimal are significant: 1000.0 says the value is known to the tenths place. A whole number like 1200 is ambiguous, so scientific notation such as 1.2 × 10³ is used to show exactly two significant figures.

Worked rounding examples

1250 sits exactly halfway between 1200 and 1300, so the tie rule decides: half to even keeps 1200 because 2 is even, while half up would give 1300. Rounding 999.96 to one place carries into a new digit and keeps the trailing zero, 1000.0.

Round half to even (banker's rounding)

Round half to even sends an exact tie to the neighbor whose last digit is even: 2.345 becomes 2.34, and 2.355 becomes 2.36. Ties then go up and down equally often, so long sums do not drift.

Rounding 0.5, 1.5, 2.5 and 3.5 to whole numbers shows the drift. Half up gives 1, 2, 3 and 4, which sum to 10; half to even gives 0, 2, 2 and 4, which sum to 8, the same as the original values.

Half to even is the default in IEEE 754 floating-point arithmetic, and NIST SP 811 uses it when the digits dropped are a 5 followed only by zeros.

The nine rounding rules

The first five rules pick the nearer neighbor and differ only at exact ties. The last four always move in one direction, however close the number is to the other neighbor.

• Half up: ties go away from zero, so 2.5 → 3 and −2.5 → −3.
• Half down: ties go toward zero, so 2.5 → 2 and −2.5 → −2.
• Half to even: ties go to the even neighbor, so 2.5 → 2 and 3.5 → 4.
• Half toward +∞: ties go to the larger neighbor, so −2.5 → −2.
• Half toward −∞: ties go to the smaller neighbor, so 2.5 → 2.
• Floor: always down, so −2.1 → −3.
• Ceiling: always up, so −2.1 → −2.
• Truncate: drops the extra digits, moving toward zero, so 1.99 → 1 and −2.1 → −2.
• Away from zero: always outward, so 2.1 → 3 and −2.1 → −3.

Python's decimal module has seven of these rules. Its names can mislead: ROUND_DOWN means truncate toward zero, and ROUND_UP means away from zero.

Common rounding mistakes

• Rounding twice. 2.345 to two places is 2.35, and rounding that to one place gives 2.4. Rounding 2.345 straight to one place gives 2.3.
• Dropping significant zeros. Writing 1000 for 1000.0 hides the precision you rounded to.
• Assuming half up makes negatives larger. Half up moves ties away from zero, so −2.5 becomes −3.
• Trusting binary floating point at ties. In Python, round(2.675, 2) returns 2.67, because 2.675 is stored as a binary number slightly below 2.675.
• Rounding intermediate results. Keep full precision through a calculation and round only the final answer.

Input formats

• Decimal places can run from −15 to 50, and significant figures from 1 to 50. The count must be a whole number.
• Numbers are handled as exact decimals, so 2.675 is a true tie and rounds to 2.68 under half up or half to even.

For numbers written as powers of ten, use the scientific notation calculator. To carry measurement uncertainty through a calculation, use the percent error and propagation calculator.