Rounding CalculatorFree online math calculator — instant results, no sign-up
Round to decimal places.
About the Rounding Calculator
This calculator rounds any real number to a specified number of decimal places using three standard approaches: nearest value, round down, and round up. It provides immediate outputs for general arithmetic, financial calculations, and engineering tasks where precision needs to be truncated or adjusted to a fixed scale.
- Number
- The numeric value to be rounded (positive, negative, integer, or decimal).
- Decimal places
- The target precision, representing the number of digits to retain after the decimal point (typically an integer ≥ 0, though negative integers round to powers of ten).
Formula and method
Factor f = 10^d Rounded = round(x × f) / f Round down = floor(x × f) / f Round up = ceil(x × f) / f
- xThe input number
- dThe number of decimal places
- fThe scaling factor, calculated as 10 raised to the power of d
The tool computes a scaling factor equal to 10 raised to the power of the decimal places. The input value is multiplied by this factor, evaluated using standard JavaScript rounding functions (Math.round, Math.floor, and Math.ceil), and then divided back by the factor.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Number3.14159265
- Decimal places2
Results
- Rounded3.14
- Round down3.14
- Round up3.15
How to use the Rounding Calculator
- 1Calculate the scaling factor f = 10^d based on the chosen decimal places.
- 2Multiply the original number x by the scaling factor f.
- 3Apply standard rounding (nearest integer, with ties rounding toward positive infinity), floor (largest integer less than or equal to the scaled value), and ceiling (smallest integer greater than or equal to the scaled value).
- 4Divide each intermediate result by the scaling factor f to restore the original decimal magnitude.
Reading your result
The 'Rounded' value shows standard nearest-neighbor rounding, rounding halves toward positive infinity. 'Round down' displays the mathematical floor, truncating downwards toward negative infinity. 'Round up' displays the mathematical ceiling, rounding strictly upward toward positive infinity.
Limitations
The calculator relies on standard IEEE 754 floating-point arithmetic, which can introduce microscopic representation discrepancies for certain base-10 fractions. It does not implement banker's rounding (round half to even) or strict directional rounding toward zero for negative numbers (truncation).
Common questions
How does standard rounding handle tie-breaks like .5?+
The nearest 'Rounded' calculation uses standard JavaScript Math.round, which rounds values ending in .5 toward positive infinity (for example, 2.5 rounds to 3, but -2.5 rounds to -2).
How do negative numbers behave when rounding down or up?+
'Round down' uses the mathematical floor function, moving toward negative infinity (e.g., -1.1 becomes -2). 'Round up' uses the ceiling function, moving toward zero for negative values (e.g., -1.9 becomes -1).
Can I use negative values for decimal places?+
Yes. Entering a negative decimal place rounds to tens (-1), hundreds (-2), thousands (-3), and so forth.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.