Rounding Calculator

How rounding works

1. Find the place you are rounding to (for example the hundredths place for 2 decimal places).
2. Look at the digit immediately to the right – the deciding digit.
3. If it is 0–4, leave the rounding digit unchanged and drop everything after it.
4. If it is 5–9, add 1 to the rounding digit (carrying if needed) and drop the rest.
5. If the deciding digit is exactly 5 with nothing after it, the result depends on the tie-breaking rule.

Example: 3.14159 to 2 decimal places. The rounding digit is 4, the deciding digit is 1, so the answer is 3.14. To 3 decimal places the deciding digit is 5 followed by 9, so 3.141 becomes 3.142.

Rounding modes compared

Half even avoids the small upward bias that half up creates when many tied values are rounded, which is why spreadsheets' statistical functions, many programming languages and some accounting systems use it.

Is 7.5 rounded up or down?

Under the usual school rule (half up) 7.5 rounds up to 8. Under banker's rounding it also becomes 8, because 8 is the nearest even number – but 6.5 would round down to 6. Always check which rule an exam, spreadsheet or invoice expects.

Rounding to the nearest 10, 100 or 1,000

The same rule applies: look at the digit to the right of the place you are rounding to. 1,250 to the nearest hundred has a deciding digit of 5, so it becomes 1,300 under half up.

Significant figures

Significant figures count from the first non-zero digit. 0.004567 to 2 significant figures is 0.0046; 45,678 to 2 significant figures is 46,000. Leading zeros are never significant, trailing zeros after a decimal point are (2.50 has three significant figures), and trailing zeros in a whole number such as 46,000 are ambiguous unless written in scientific notation (4.6 × 10⁴).

Why software sometimes rounds 1.005 to 1.00

Computers store most decimals in binary floating point, and 1.005 is actually stored as 1.00499999999999989… Rounding that value to two places gives 1.00, not 1.01. This calculator rounds the decimal number you typed, so 1.005 correctly becomes 1.01 under half up. In spreadsheets and code, use decimal types or round in steps if exact results matter.

Rounding money and measurements

• Round only at the final step – rounding intermediate results adds up small errors.
• For money, round to the smallest currency unit (cents); totals of rounded line items may differ by a cent from the rounded total.
• For measurements, match the precision of your least precise input (a length measured to 0.1 cm should not be reported to 0.001 cm).

Rounding in Excel, Google Sheets and code

Because tools use different tie rules, the same data can give slightly different totals in a spreadsheet and in code. Pick one rule and apply it consistently.

Sources

1. NIST – Guide for the Use of the International System of Units (SP 811), rounding rules — nist.gov/pml/special-publication-811