Rounding Calculator
Round numbers to decimal places, significant figures or a nearest multiple, in five rounding modes.
Inputs
Half-up is what most people learned at school. Half-even prevents bias over many rounded values.
Rounded value
3.1400000000
Absolute rounding error
0.0015926500
How far the rounded value is from the original.
Percent rounding error
0.050696%
Step by step
Input value
= 3.14159265
Round to 2 decimal places
half-up mode applied to 3.14159265
= 3.14
Rounding error
|3.14 − 3.14159265|
= 0.001593
How it works
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
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.