Rounding replaces a number with a simpler one close to it: 3.14159 becomes 3.14 to two decimal places, and 48,762 becomes 49,000 to the nearest thousand. The basic school rule is to look at the first digit you are dropping. If it is 5 or more, round up; otherwise keep the digit you have. This rounding calculator applies that rule and four others, to any number of decimal places, to the nearest 10, 100 or 1,000, or to a number of significant figures. It shows all five results side by side so you can see where they differ.
Rounding matters in grades, where 89.5 may or may not become a 90 (see the letter grade calculator), and in unit conversions such as the area converter, where you should round only at the end.
How to use the rounding calculator
- Enter the number.
- Choose decimal places or significant figures.
- Enter the number of places: 2 for hundredths, 0 for a whole number, −1 for the nearest ten, −2 for the nearest hundred, −3 for the nearest thousand.
- Pick a rounding rule, or compare all five in the table.
Formula
Here k is the number of decimal places (negative for tens, hundreds and so on). For significant figures, k = figures − 1 − floor(log₁₀|x|). The rules differ only in what "round" does with the leftover fraction:
- Half up: a fraction of .5 or more goes up in size (away from zero). This is the method taught in school.
- Half to even: an exact .5 goes to the nearest even digit, so 2.5 → 2 and 3.5 → 4. Other fractions round normally.
- Ceiling / floor: always toward +∞ or −∞.
- Truncate: drop the extra digits (toward zero).
Worked example
- 3.14159 to 2 decimal places: the next digit is 1 (less than 5), so 3.14.
- 2.675 to 2 places: half up gives 2.68, and half to even also gives 2.68 because 8 is even. 2.665 gives 2.67 half up but 2.66 half to even.
- 48,762 to the nearest thousand (−3): the hundreds digit is 7, so 49,000.
- 0.004567 to 2 significant figures: the first non-zero digit is 4, so 0.0046.
Why banker’s rounding exists
If you always round exact halves up, a long column of numbers ending in .5 is biased upwards: every tie adds a little. Rounding halves to the nearest even digit sends about half the ties up and half down, so totals stay closer to the true sum. Many spreadsheet and programming functions, statistical packages and accounting systems offer it for that reason. The NIST Guide for the Use of the International System of Units (SP 811) also discusses rounding converted values so they don't imply more precision than the original.
Significant figures in brief
Significant figures count the digits that carry meaning, starting from the first non-zero digit. 0.004567 has four, and so does 4,567. Trailing zeros in a whole number are ambiguous (does 1,200 have two or four?), which is why scientists use scientific notation (1.2 × 10³). When multiplying or dividing measurements, a common rule is to round the result to the fewest significant figures among the inputs. When adding, round to the fewest decimal places.
| Number | Sig figs | To 2 sig figs |
|---|---|---|
| 4,567 | 4 | 4,600 |
| 0.004567 | 4 | 0.0046 |
| 12.05 | 4 | 12 |
| 98,500 | 3 (assumed) | 99,000 (half up) / 98,000 (half even) |
Caveats and assumptions
- Computers store most decimals in binary, so a typed 2.675 is really 2.67499999…; this calculator corrects for that and rounds the number as written.
- Round only once, at the end. Rounding intermediate steps can change the final answer.
- Your school, lab or business may require a specific rule; check before using banker’s rounding for homework.
- Very large or very small numbers beyond about 15 significant digits lose precision in browsers.
Frequently asked questions
How do I round to two decimal places?
Look at the third decimal digit. If it is 5 or more, add one to the second digit; otherwise leave it. 7.846 → 7.85 and 7.843 → 7.84.
How do I round to the nearest hundred?
Look at the tens digit. If it is 5 or more, round up. 1,250 → 1,300 and 1,249 → 1,200. Enter −2 for places above.
What is banker’s rounding?
Rounding exact halves to the nearest even digit (2.5 → 2, 3.5 → 4) so that ties don’t bias totals upwards. Other values round normally.
Does 0.5 round up or down?
Under the usual school rule it rounds up to 1. Under banker’s rounding it rounds to 0, the nearest even number.
How do I round negative numbers?
Round half up treats negatives symmetrically, so −2.5 becomes −3 (away from zero). "Always round up" (ceiling) moves toward positive infinity, so −2.5 becomes −2.
Sources
- OpenStax Prealgebra 2e — 1.1 Introduction to Whole Numbers (rounding) — rounding whole numbers
- OpenStax Prealgebra 2e — 5.1 Decimals (rounding decimals) — rounding decimals
- NIST Special Publication 811 — Guide for the Use of the International System of Units — rounding converted numerical values
This calculator gives estimates for planning and education. Check measurements, local codes, supplier specs and your school's official policy before relying on a result. See our disclaimer and how we build and check calculators.