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Rounded Value
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Enter a number to round
Nearest Integer
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Floor
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Ceiling
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Truncated
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Difference
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Error %
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Decimal PlacesStandardFloorCeiling

Round any number to a chosen number of decimal places or significant figures using standard, banker's, floor, ceiling, or truncate rules.

How It Works

How Rounding Calculator Works

Standard ("half-up") rounding looks at the digit right after your chosen cutoff: if it is 5 or more, the last kept digit rounds up; otherwise it stays the same. Floor always rounds down toward negative infinity, ceiling always rounds up toward positive infinity, and truncate simply chops off the extra digits without rounding at all — each method can give a different answer for the same number.

Banker's rounding (also called "round-half-to-even") is a variant used to avoid statistical bias when rounding many numbers: when the digit being dropped is exactly 5, it rounds to whichever neighboring value is even, rather than always rounding up. This matters more for repeated rounding across large datasets than for a single calculation.

Switching to "significant figures" mode changes what is being preserved — instead of a fixed number of decimal places, it keeps a fixed number of meaningful digits regardless of where the decimal point falls, which matters for very large or very small numbers where decimal-place rounding would lose or add unwanted precision.

Worked Example

See It In Action

Rounding 3.14159 to 2 decimal places using the standard method: the digit after the cutoff is 1 (from "3.14159"), which is less than 5, so it rounds down to 3.14. The difference between the rounded and original value is −0.00159, an error of about 0.05%. Flooring the same number to 2 decimal places also gives 3.14, while the ceiling gives 3.15.
Real-World Use Cases

Who Uses Rounding Calculator and Why

  • Rounding a financial total to the nearest cent before displaying it on an invoice.
  • Reducing a long decimal measurement to a sensible number of significant figures for a lab report.
  • Applying banker's rounding across a large batch of values to avoid the small upward bias standard rounding introduces over many numbers.
  • Flooring or ceiling a calculated quantity when a real-world constraint requires a whole number that can't go over (ceiling) or under (floor) the true value.
Common Mistakes

Mistakes to Avoid

  • Using truncate when rounding was actually intended — truncate simply deletes extra digits and always moves the value toward zero, which is never as accurate as proper rounding.
  • Applying standard (half-up) rounding to a large repeated dataset where banker's rounding would be more appropriate, introducing a small systematic bias across many values.
  • Confusing decimal places with significant figures — a number like 0.00456 has 5 decimal places but only 3 significant figures, and rounding to "2 decimal places" versus "2 significant figures" gives different results.
Pro Tips

Tips for Best Results

  • Switch to significant-figures mode for very large or very small numbers, where a fixed decimal-place cutoff would lose or add unwanted precision.
  • Use floor or ceiling instead of standard rounding whenever the real-world situation can't tolerate going over or under the true value (like rounding up the number of boxes needed to fit an inventory).
Troubleshooting

Fixing Common Problems

Floor, ceiling, and standard rounding are all giving different answers for the same number. — That's expected — each method follows a different rule (nearest, always down, always up), so they only agree when the number is already at or very near the rounding cutoff.

I'm not sure which decimal place standard rounding rounded from. — Check the digit immediately after your chosen cutoff — 5 or higher rounds the last kept digit up, anything lower leaves it unchanged.

Glossary

Terms Explained

Significant figures: All meaningful digits in a number regardless of where the decimal point falls, as opposed to decimal places, which count only digits after the point.

Banker's rounding: A round-half-to-even method that rounds an exact .5 to whichever neighboring value is even, used to reduce bias when rounding many numbers.

FAQ

Frequently Asked Questions

What is the difference between rounding and truncating?
Rounding adjusts the final kept digit up or down based on what comes after it, aiming for the closest representable value. Truncating simply deletes everything past the cutoff with no adjustment, which always moves the value toward zero and is never more accurate than rounding.
When should I use banker's rounding instead of standard rounding?
Banker's rounding is preferred in finance and statistics when rounding large volumes of numbers, because always rounding 0.5 upward introduces a small systematic bias over many values, while rounding to the nearest even digit balances that bias out.
What are significant figures and how do they differ from decimal places?
Decimal places count digits strictly after the decimal point. Significant figures count all meaningful digits in a number regardless of the decimal point's position — so 0.00456 has 3 significant figures but 5 decimal places, and 4,560 has 3 significant figures but 0 decimal places.
Why does the error percentage matter?
The error percentage shows how much the rounded value differs from the original, relative to the original's size. It is most useful for judging whether a rounding choice is precise enough for a given purpose, such as financial reporting or scientific measurement.