Rounding Calculator
Round any number to a specified number of decimal places.
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How to use this tool
- Enter number and decimal places in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your rounded value and the full breakdown beneath it.
Round any number to the desired number of decimal places using standard rounding rules.
Formula
Rounded = round(value × 10d) ÷ 10d
where d is the number of decimal places. Computed as: factor = 10d, then result = Math.round(value × factor) / factor.
How it works
This calculator rounds any real number to a specified number of decimal places using the standard half-up rounding rule. It scales the number up by a power of 10, applies integer rounding, then scales back down — the same method used in most programming languages and calculators. It is accurate for common precision needs; very large numbers with many decimal places may show minor floating-point artefacts.
Worked example
- Value = 3.14159, decimal places d = 2.
- Factor = 10² = 100.
- Scale up: 3.14159 × 100 = 314.159.
- Round: Math.round(314.159) = 314.
- Scale down: 314 ÷ 100 = 3.14.
3.14159 rounded to 2 decimal places = 3.14.
Common mistakes to avoid
- Rounding intermediate results during a multi-step calculation instead of only at the final step, causing cumulative rounding error.
- Confusing "round to 2 decimal places" with "round to 2 significant figures"; 0.00456 rounded to 2 decimal places is 0.00, not 0.0046.
- Expecting standard 0.5-rounds-up behavior in all languages; some use banker's rounding where 2.5 rounds to 2, not 3.
Key terms
- Decimal places
- The number of digits to keep after the decimal point in the rounded result.
- Half-up rounding
- The convention where values exactly halfway between two options are rounded up. For example, 2.5 rounds to 3.
- Scaling factor
- 10 raised to the power of the desired decimal places (e.g. 10² = 100 for 2 d.p.), used to shift the decimal point before integer rounding.
- Floating-point
- The binary representation of real numbers in computers. Very long decimals may not round-trip perfectly, so results should be interpreted to the requested precision only.
Frequently asked questions
- How does rounding work?
- When the digit after the rounding position is 5 or greater, round up; otherwise round down. For example, 3.14159 rounded to 2 decimals = 3.14.