Rounding Calculator
Round a number to a set number of decimal places, or to the nearest multiple of any number (10, 100, 1000, or a custom value) — with Normal, Round Down, and Round Up modes.
Calculator verified • Last updated: August 2026
Number to Round
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How Rounding Works
Rounding replaces a number with a nearby "simpler" value — fewer decimal places, or the nearest multiple of some round number — according to a consistent rule. This calculator supports two ways of choosing that target (decimal places, or nearest multiple of N) and three directions for handling the value in between (Normal, Down, and Up).
Decimal Places Mode
x: the original number.
d: the number of decimal places to keep.
For example, rounding 3.14159 to 2 decimal places: multiply by 100 to get 314.159, round to the nearest whole number to get 314, then divide back by 100 to get 3.14.
Nearest Multiple Mode
x: the original number.
N: the multiple to round to (for example, 10, 100, or 1000).
For example, rounding 1,247 to the nearest 100: divide by 100 to get 12.47, round to the nearest whole number to get 12, then multiply back by 100 to get 1,200.
Normal, Round Down, and Round Up — What Each Mode Means
Normal mode uses standard round-half-up rounding, the everyday rule taught in school: look at the next digit being dropped, and round up if it's 5 or higher, down otherwise. This matches JavaScript's built-in Math.round behavior. Round Down (floor) always moves toward negative infinity regardless of the dropped digits — 2.9 rounds down to 2, but so does negative 2.1, which rounds down to negative 3. Round Up (ceiling) always moves toward positive infinity the same way — 2.1 rounds up to 3, and negative 2.9 rounds up to negative 2. Down and Up are not the same as "toward zero" and "away from zero" for negative numbers, which trips people up if they assume floor always means "toward zero."
Why 1.005 Rounded to 2 Decimals Can Give a Surprising Answer
This is one of the most common "is this calculator broken?" moments in programming, and it isn't a bug — it's how binary floating-point numbers work. Computers (JavaScript included) store most decimal fractions as an approximation, since values like 0.005 can't be represented exactly in binary, the same way one-third can't be written exactly as a finite decimal. The number actually stored for "1.005" is very slightly less than 1.005, so a mathematically correct round-half-up on the stored value rounds down to 1.00, not up to 1.01 as pencil-and-paper math would suggest. This isn't specific to this calculator — it affects any software doing floating-point decimal rounding, including spreadsheets and most programming languages, and is one of the more genuinely useful things to understand about how computers handle decimal numbers.
Common Rounding Mistakes
Rounding a number more than once in a chain of calculations (rounding an intermediate result, then rounding again at the end) can compound small errors and drift from the answer you'd get by rounding only the final result — keep full precision through intermediate steps when possible, and round only at the end. Confusing "round down" with "round toward zero" is another common mix-up, since they behave identically for positive numbers but oppositely for negative ones. Rounding currency values with plain decimal-place rounding instead of a currency-aware method can also introduce tiny cumulative errors across many transactions, which is why financial systems often use specialized rounding rules.
Rounding Terms You Should Know
Round-Half-Up — the everyday rounding rule where a value exactly halfway between two targets rounds to the higher one; this calculator's Normal mode.
Floor — rounding a number down to the nearest allowed value, always moving toward negative infinity.
Ceiling — rounding a number up to the nearest allowed value, always moving toward positive infinity.
Truncation — cutting off extra digits without rounding at all, equivalent to always rounding toward zero.
Floating-Point — the binary format most computers use to store decimal numbers, which can only approximate most non-whole decimal values.
Frequently Asked Questions
Why does rounding 1.005 to 2 decimal places sometimes give 1.00 instead of 1.01?
Most decimal values like 1.005 can't be stored exactly in binary floating-point, the number format almost all software (including JavaScript) uses. 1.005 is actually stored as a value fractionally below 1.005, so standard rounding correctly rounds that stored value down to 1.00 — the input never actually reaches the halfway point.
What is the difference between rounding and truncating?
Rounding picks the nearest allowed value, which can go up or down depending on the digit being dropped. Truncating simply cuts off the extra digits without checking them, which is the same as always rounding toward zero regardless of what those digits were.
What does round-half-up mean?
Round-half-up means that when a number is exactly halfway between two rounding targets, it rounds to the higher one. This is the everyday rounding rule taught in school and is what this calculator's Normal mode uses, matching standard JavaScript rounding behavior.