Rounding Calculator Online Free Tool
Rounding Calculator
Rounding Calculator
Instructions: Enter any number and select a precision level. The calculator will show you the result using different rounding methods: normal rounding (rounds 0.5 up), round up (ceiling), round down (floor), and truncate. You can round to decimal places, whole number places (tens, hundreds, etc.), or common fractions (1/2, 1/4, 1/8, etc.).
Rounding simplifies a number to a specified precision by replacing it with the nearest value at the chosen level of precision. This calculator rounds to any number of decimal places or significant figures and applies any rounding rule: round half up (standard), round half down, round half to even (banker's rounding), or always round toward zero.
Rounding Rules
The most common rule is "round half up": if the digit being dropped is 5 or more, round up. If less than 5, round down. Other rules exist for specific applications.
Round 3.745 to 2 decimal places: "Round half up": 3.75 "Round half down": 3.74 "Round half to even" (banker's): 3.74 (because 4 is even) Significant figures: 3,745 to 3 sig figs = 3,750 (All non-zero digits count; trailing zeros matter only with a decimal point)
Decimal Places vs Significant Figures
Decimal places count positions after the decimal point. Significant figures count meaningful digits regardless of decimal position. Context determines which applies: financial calculations typically use decimal places; scientific measurements use significant figures.
| Number | 2 Decimal Places | 3 Significant Figures |
|---|---|---|
| 3.14159 | 3.14 | 3.14 |
| 0.00456789 | 0.00 | 0.00457 |
| 12345.678 | 12345.68 | 12300 |
| 1234 | unchanged | 1230 |
Frequently Asked Questions
What is banker's rounding?⌄
Banker's rounding (round half to even) rounds 0.5 to the nearest even digit: 2.5 rounds to 2, 3.5 rounds to 4, 4.5 rounds to 4, 5.5 rounds to 6. This eliminates the statistical bias of always rounding 0.5 up, which can cause systematic over-counting in large datasets. It is used in financial and statistical calculations.
How many significant figures should I use?⌄
Use the same number of significant figures as your least precise measurement. If you are multiplying 3.5 (2 sig figs) × 1.234 (4 sig figs), the result should be rounded to 2 sig figs: 4.3. Your result is only as precise as your least precise input. Reporting 4.319 would imply more precision than actually exists.
Why do stores always round prices up?⌄
Retailers use asymmetric rounding (always round up) to avoid charging less than the calculated price. This is different from mathematical rounding and is a business decision. Some jurisdictions require round half up for billing. Cash transactions in countries that eliminated small coins (like Canada, eliminating the penny) use Swedish rounding (round to nearest 5-cent increment).
Can rounding cause significant errors?⌄
Yes, especially through accumulated rounding error. If many small rounding errors are added together, the cumulative effect can be large. This is why spreadsheets may show unexpected totals when column values are displayed as rounded but stored at full precision. In scientific calculations, interval arithmetic tracks the accumulated rounding error explicitly.