Rounding Calculator
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How Rounding Works
Rounding replaces a number with a nearby value that has fewer significant digits, according to a defined rule. The most common convention — round half up (also called "round half away from zero" for positive numbers) — looks at the first digit being dropped: if it's 5 or greater, the last kept digit increases by one; if it's 4 or less, the last kept digit stays the same. This calculator supports that standard method as well as several alternatives used in specific fields, including round half to even (banker's rounding), which statisticians and accountants prefer because it eliminates the small upward bias that round-half-up introduces over many repeated roundings.
Decimal Places vs. Significant Figures vs. Place Value
Rounding to a number of decimal places fixes how many digits appear after the decimal point (e.g. 3.14159 to 2 decimal places is 3.14). Rounding to significant figures counts meaningful digits starting from the first non-zero digit, regardless of where the decimal point falls (e.g. 0.0031415 to 3 significant figures is 0.00314, and 31415 to 3 significant figures is 31400). Rounding to a place value (tens, hundreds, thousands) is common in everyday estimation, such as rounding a price to the nearest dollar or a population to the nearest thousand.
When Precision Actually Matters
Excessive rounding early in a multi-step calculation can compound into meaningful error by the final answer — a common mistake is rounding intermediate results instead of carrying full precision through and rounding only at the end. If you're working with measurement data and need to track how rounding and instrument precision affect your results, see the percent error calculator and the scientific notation calculator for expressing very large or very small rounded values cleanly.
Frequently Asked Questions
What is the difference between rounding to decimal places and significant figures?
Decimal places count digits after the decimal point regardless of the number's size (3.14159 rounded to 2 decimal places is 3.14). Significant figures count meaningful digits starting from the first non-zero digit, so they scale with the number's magnitude (0.0031415 to 3 significant figures is 0.00314, while 31415 to 3 significant figures is 31400).
What is round half to even, and why would I use it instead of round half up?
Round half to even, also called banker's rounding, rounds a value that is exactly halfway between two options to whichever neighbor has an even last digit (2.5 rounds to 2, 3.5 rounds to 4). Unlike round half up, which always rounds midpoint values upward, this method avoids introducing a systematic upward bias when many values are rounded and summed, which is why it is the default in some financial and statistical calculations.