Rounding Calculator
Rounding is the process of replacing a number with a nearby value that is simpler or more convenient to work with, and this calculator covers every common rounding scenario in one place. You can round any number to a specific number of decimal places, or snap it to the nearest whole number, ten, hundred, thousand, or any other multiple you specify. The standard rounding rule used here is half-up: if the digit after your chosen cut-off point is 5 or more, the last kept digit increases by one; if it is 4 or less, the last kept digit stays the same. This is the rule taught in schools and used in everyday maths, accounting, and measurement. The calculator also shows you the ceiling, rounding always upward to the next step regardless of the following digit, and the floor, rounding always downward. These matter when the direction of error is important: you round quantities of materials up so you always have enough, and you might round a discount down so you never accidentally give more than intended. The tool also tells you the direction of the rounding that was applied, whether the result went up, down, or stayed the same. Enter any number and select your rounding target from the two options: a number of decimal places from zero to five, or a nearest multiple such as 10 or 100. Both options update in real time as you type. This calculator is useful for students checking homework, accountants tidying figures, engineers expressing measurements to the right precision, and anyone who regularly needs to round numbers clearly and correctly.
How it works
When rounding to decimal places, the calculator shifts the number by the chosen power of ten, applies the standard half-up rule using Math.round, then shifts back. When rounding to a nearest multiple, it divides the number by the multiple, rounds to the nearest whole number, and multiplies back. The ceiling always uses Math.ceil (the next step up) and the floor always uses Math.floor (the next step down). The direction is determined by comparing the rounded result to the original value.
Worked example
Enter 3.14159 and select 2 decimal places. The digit after the second decimal place is 1, which is below 5, so the result rounds down to 3.14. The ceiling to 2 decimal places is 3.15 (always the next step up) and the floor is 3.14 (always the next step down). If you select the nearest 10, the result is 0 because 3.14159 is closer to 0 than to 10.
Related calculators
- Significant Figures Calculator: round a number to the correct number of significant figures.
- Scientific Notation Calculator: convert a number to scientific notation.
- Decimal to Fraction Calculator: convert a decimal to its simplest fraction.
- Percent Error Calculator: measure how far a value deviates from a true value.