Rounding Calculator
Round any number to a decimal place, significant figures, or a custom nearest-multiple across 9 rounding modes. For example, 3.14159 rounds to 3.14 at the nearest hundredth. Exact ties matter: 2.5 rounds to 3 under half up (this calculator's convention, matching Excel), but to 2 under half to even (banker's rounding). And because this calculator parses your digits directly instead of a raw binary float, 0.145 correctly rounds to 0.15 — not the 0.14 a naive floating-point calculator can silently return.
Half up — ties round away from 0 (Excel ROUND(), US-school default; see note on calculator.net's different convention)
3.14
3.14159 rounded to hundredths (2 decimal places — cents)
The digit right after the target precision is 1, which is less than 5, so the value rounds down to the nearest value — no tie involved.
Note on negative numbers: "Half up" and "Half away from zero" are the SAME rule in this calculator — on a tie, the magnitude always increases (−2.5 → −3), matching Excel's ROUND() function. Some other calculators define "half up" as rounding ties toward the more positive neighbor instead (−2.5 → −2) — if a result here disagrees with another tool for a negative tie, this is why. See the floating-point section below for why 0.145 rounds correctly to 0.15 here.
Rounded with a decimal-string engine, not a raw binary float — see why that matters below. How we calculate →
How to round a number — the decisive digit
Every rounding decision comes down to one digit: the one immediately to the right of the place you're rounding to. Look at 3.14159 rounded to the nearest hundredth (2 decimal places): the digit right after the hundredths place is the thousandths digit, 1. Since 1 is less than 5, the hundredths digit stays put and everything after it is dropped: 3.14159 → 3.14. No tie, so every rounding mode agrees on this one.
If that decisive digit is 5 or more, the kept digit goes up by one. If it's exactly 5 with nothing but zeros after it, you've hit an exact tie — and that's where rounding "modes" start to disagree, because there's no single universal rule for which way a tie should break. That disagreement is the whole reason a calculator needs to let you pick a mode instead of assuming one.
The 9 rounding modes, compared on the same three numbers
The clearest way to see how the modes differ is to run the exact same ambiguous inputs — a positive tie (2.5), a negative tie (−2.5), and the classic decimal pitfall (0.145) — through every mode. Two calculators in the top search results (calculator.net and calculatorsoup/Excel) actually define "half up" differently for negative numbers, which is exactly the kind of disagreement below.
2.5 to the nearest whole number: Half up / Half away from zero → 3. Half down → 2. Half toward zero → 2. Half to even (banker's) → 2. Half to odd → 3. Ceiling → 3. Floor → 2. Truncate → 2.
−2.5 to the nearest whole number: Half away from zero (and Calcuris's "Half up") → -3. Half to even (banker's) → -2. Half toward zero → −2. Ceiling → −2. Floor → −3. Truncate → −2. (A calculator that defines "half up" as calculator.net does — ties toward +infinity — would instead give −2.5 → −2; see the note on negative numbers above the calculator.)
0.145 to the nearest hundredth: the mathematically correct half-up/half-away-from-zero answer is 0.15 — but a calculator built on raw binary floating-point arithmetic can silently return 0.14 instead. See the next section for why.
The floating-point pitfall: why 0.145 can round to 0.14 on the wrong engine
Computers store decimal numbers like 0.145 in binary (IEEE 754 double-precision floats), and most decimal fractions simply can't be represented exactly in binary — the same way 1/3 can't be written exactly in decimal. The value actually stored for 0.145 is approximately 0.144999999999999995559..., a hair below the true 0.145.
Run that through a naive rounding routine and it breaks: in a standard JavaScript engine, (0.145).toFixed(2) returns "0.14", not "0.15" — because the routine is rounding the corrupted binary value, which is genuinely just under the tie point, not the decimal number you typed. The same bug affects Math.round(1.005 * 100) / 100, which returns 1 (i.e. "1.00") instead of the expected 1.01.
Calcuris's engine never multiplies your number by a power of ten and rounds the resulting float. Instead it parses the digits you typed as a string, finds the decisive digit directly in that string, and applies the rounding rule to the digits themselves — the binary float never enters the tie decision. That's why this calculator correctly returns 0.145 → 0.15 under half-up, the answer you'd get by hand, not the 0.14 a float-based tool can silently produce. One competitor in the search results (calculator.goldsupplier.com) advertises "eliminating floating-point errors" without explaining the mechanism — this is that mechanism, shown with the actual failing example.
Banker's rounding (half to even) — and why finance and statistics use it
Half-up and half-away-from-zero always push ties in a fixed direction, which means if you round thousands of numbers with a lot of exact .5 ties, the results drift slightly upward on average — a systematic bias. Half to even (also called banker's rounding or Gaussian rounding) breaks each tie toward whichever neighbor has an even last digit instead: 2.5 → 2 (2 is even), but 3.5 → 4 (4 is even). Over a large data set, ties end up split roughly 50/50 between rounding up and down, which cancels out the bias.
That's why half-even is the default tie-breaking rule inside IEEE 754 binary floating-point arithmetic itself (used internally by virtually every programming language's number type), and why it's the standard convention in accounting, statistics, and scientific computing when many values get rounded to the nearest cent or unit and the cumulative error matters. It is NOT what most people expect from a single everyday rounding — for that, half away from zero (this calculator's "half up") matches what's taught in US schools and what Excel's ROUND() function does.
Significant figures vs. decimal places
Rounding to a number of decimal places counts digits after the decimal point, no matter how big or small the number is. Rounding to significant figures counts meaningful digits starting from the first nonzero digit, regardless of where the decimal point falls — it's the right choice when the size of the number itself varies a lot, like in scientific measurements.
Example: 0.004566 rounded to 3 significant figures is 0.00457 — the leading zeros (0.00) aren't significant, so counting starts at the first "4". Rounded to 3 decimal places instead, the same number would give a very different (and less useful) result of 0.005, because decimal places don't know or care where the first meaningful digit is.
Rounding to a custom multiple — including cash rounding
Sometimes you don't want the nearest tenth or hundredth — you want the nearest quarter, nearest nickel, or nearest 5 units. That's "round to nearest multiple": divide by the multiple, round to the nearest whole number, then multiply back. 7.36 rounded to the nearest 0.25 is 7.25.
A common real-world case is cash rounding — several countries have eliminated the 1-cent coin and round cash totals to the nearest 5 cents. $19.83 rounded to the nearest nickel ($0.05) is $19.85. Only one calculator observed in the search results for this topic (calculator.goldsupplier.com) offers a custom-multiple mode at all — it's a genuinely underserved feature for a widely searched term.
Frequently asked questions
How do I round to the nearest whole number?
Look at the first decimal digit. If it's 5 or more, round the whole-number part up by one; if it's less than 5, leave it unchanged and drop everything after the decimal point. 7.3 rounds to 7; 7.6 rounds to 8. For an exact tie like 7.5, the result depends on the rounding mode — 8 under half up / half away from zero, or 8 under half to even too in this case since 8 is even (but 6.5 under half to even rounds to 6, not 7).
Is 7.5 rounded up or down?
Under the default "half up" (half away from zero) convention used by this calculator, Excel, and most US schools, 7.5 rounds up to 8. Under half to even (banker's rounding), 7.5 also rounds to 8, because 8 is the even neighbor. The two conventions only disagree when the even neighbor is the LOWER one — for example 6.5 rounds to 6 under half-to-even but 7 under half away from zero.
What does 2.47 round to at the nearest tenth?
2.47 rounded to the nearest tenth (1 decimal place) is 2.5 — the digit after the tenths place is 7, which is 5 or greater, so the tenths digit (4) rounds up to 5.
Why does 0.145 round to 0.15 here but 0.14 on some calculators?
0.145 is exactly halfway between 0.14 and 0.15, so the mathematically correct half-up answer is 0.15. But 0.145 can't be stored exactly in binary floating-point — it's actually held as a value fractionally below 0.145 — so a calculator that rounds the raw binary float (a common shortcut) can silently return 0.14 instead. This calculator rounds the decimal digits you typed directly, without ever converting through a binary float, so it returns the mathematically correct 0.15.
What is banker's rounding and when should I use it?
Banker's rounding (half to even) breaks exact ties by rounding to whichever neighbor has an even last digit, instead of always rounding up. It's used in accounting and statistics because it avoids the small but systematic upward bias that half-up rounding creates when many .5 ties are rounded the same direction across a large data set.
What's the difference between rounding to decimal places and significant figures?
Decimal places count digits after the decimal point regardless of the number's size. Significant figures count meaningful digits starting from the first nonzero digit, wherever it falls. 0.004566 rounded to 3 significant figures is 0.00457 (counting from the first "4"), but rounded to 3 decimal places it would be 0.005 — a much less precise result for a small number.
Why do -2.5 and 2.5 round differently on different calculators?
Because "round half up" is genuinely ambiguous for negative numbers across different tools. This calculator defines half up as "ties away from zero" (Excel's convention: -2.5 → -3), matching what most US users expect. Some other calculators define half up as "ties toward positive infinity" instead (-2.5 → -2). Neither is more "correct" mathematically — they're different, valid conventions, which is why this calculator documents the choice explicitly rather than leaving it unlabeled.
How do I round to the nearest 5 or nearest 0.25?
Divide the number by the multiple you want (5, 0.25, 0.05, etc.), round the result to the nearest whole number, then multiply back by the multiple. Use the "Round to nearest multiple" mode above — 7.36 to the nearest 0.25 is 7.25, and it also handles cash rounding to the nearest nickel.
Researched & verified by the Calcuris Data & Research Team. How we build and check our tools →