Rounding Calculator
Round to decimals, significant figures or the nearest multiple, with every rounding mode.
About Rounding Calculator
Rounding replaces a number with a nearby value that is simpler or fits a required precision. The five modes differ only in the tie-breaking rule: half-up (the school rule) always rounds 0.5 away from zero; half-even (IEEE 754) rounds 0.5 to the nearest even number, eliminating statistical bias; ceiling and floor unconditionally round up or down; truncate drops the fractional part without regard to sign.
Formulas
Decimal rounding
x_rounded = round(x × 10^n, mode) / 10^n
- x
- Input value
- n
- Number of decimal places
Significant figures
places = sigFigs − floor(log₁₀|x|) − 1
- d
- Required significant figures
- x
- Input value
Nearest multiple
x_rounded = round(x / multiple) × multiple
- m
- The multiple to round to
Worked example
With the default values below, Rounding Calculator returns Rounded value of 3.1400000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number to round
- 3.141593
- Round toone of Decimal places, Significant figures, Nearest multiple
- Decimal places
- Decimal placesaccepts 0–20
- 2
- Significant figuresaccepts 1–20
- 3
- Round to nearest multiple ofminimum 0
- 0.25
- Rounding modeone of Half-up (standard), Half-even (banker's rounding), Ceiling (always up), Floor (always down), Truncate (toward zero)
- Half-up (standard)
Results
- Rounded value
- 3.1400000000
- Absolute rounding errorHow far the rounded value is from the original.
- 0.0015926500
- Percent rounding error
- 0.050696%
Step by step
- 1Input value= 3.14159265
- 2Round to 2 decimal places= 3.14
- 3Rounding error= 0.001593
Assumptions and limits
- The result is derived only from the 6 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the difference between half-up and half-even?
Half-up is the everyday 'round 0.5 up' rule. Over a large dataset, consistently rounding 0.5 upward introduces a slight positive bias. Half-even (banker's rounding) avoids this by rounding 0.5 to whichever neighbour is even: 2.5 → 2, 3.5 → 4. It is the IEEE 754 default and is used in financial and scientific computing.
What are significant figures?
Significant figures are the meaningful digits of a measurement, starting from the first non-zero digit. The number 0.00340 has 3 significant figures (3, 4, 0). Trailing zeros after a decimal point are significant.
When would I round to a nearest multiple?
Rounding to a nearest multiple is useful for prices (nearest $0.05), time intervals (nearest 15 minutes), and measurements on scaled instruments. For example, 73 rounded to the nearest 10 is 70, and 3.14 rounded to the nearest 0.25 is 3.25.