Rounding Calculator
Round any number to a number of decimal places, significant figures, or the nearest multiple — with standard, up, down or banker's rounding.
How to use this calculator
- 1Enter your number.
- 2Choose whether to round by decimal places, significant figures, or to the nearest multiple of something (like the nearest 5 or nearest 0.25).
How the calculation works
Standard rounding: round half away from zero. Banker's rounding: round half to the nearest even digit.- Decimal places
- How many digits to keep after the decimal point
- Significant figures
- How many meaningful digits to keep, counted from the first non-zero digit
- Nearest multiple
- The step size to round to, such as the nearest 5, 10 or 0.25
Banker's rounding is used by many financial and statistical systems because rounding 0.5 up every time introduces a small systematic upward bias across many roundings — rounding to even cancels that bias out on average.
Significant figures count from the first non-zero digit, so 0.004205 to 3 significant figures is 0.00421, not 0.004 — leading zeros never count.
Worked example
3.14159 to 2 decimal places
- 1.3.14159 × 100 = 314.159, which rounds to 314, so 314 ÷ 100 = 3.14.
Result: 3.14
What rounding is actually doing
Rounding replaces an exact value with the nearest value that fits a chosen level of precision — the nearest whole number, the nearest cent, the nearest thousand, or the nearest value in any other step size you choose. It is not a calculation that finds a "wrong" or "right" answer so much as a deliberate trade: some precision is given up in exchange for a number that is shorter, easier to communicate, or matches how precisely something can actually be measured or paid.
Every rounding rule needs to decide two things: how far to round (the precision), and what to do when a value sits exactly halfway between two candidates. Those two questions are exactly what the "round to" mode and "rounding method" options on this calculator control.
Decimal places versus significant figures
Rounding to a fixed number of decimal places keeps the same number of digits after the decimal point regardless of a number's size — 3.14159 and 31415.9 both round to one decimal place the same way. Significant figures work differently: they count meaningful digits starting from the first non-zero digit, so the precision scales with the size of the number itself. Rounding 0.0031415 and 31415 to three significant figures gives 0.00314 and 31400 respectively — very different numbers of decimal places, but the same relative precision. Scientists and engineers favour significant figures specifically because a measurement's precision is usually relative to its size, not tied to a fixed number of decimal places.
Why the halfway case needs its own rule
A number like 2.5 sits exactly between 2 and 3, so no rounding rule is more "correct" than another for it — each one is a deliberate convention rather than a mathematical necessity.
- Round half away from zero — the everyday default taught in school: 2.5 rounds to 3, and −2.5 rounds to −3. Simple, but repeated over many values it introduces a small, consistent upward bias.
- Round half to even (banker's rounding) — rounds a halfway value to whichever neighbouring number is even — 2.5 rounds to 2, but 3.5 rounds to 4. Because "which neighbour is even" is roughly a coin flip across many numbers, the bias from the rule above cancels out on average, which is why this is the default in many financial systems and in the floating-point standard used by most computers.
- Always round up or down — used less for accuracy and more for a deliberate business or safety margin — rounding a shipping weight up, or a maximum load rating down, so the rounded figure is never on the risky side of reality.
Where rounding quietly matters
Rounding decisions rarely make headlines, but they shape real outcomes wherever exact values get truncated for display or storage.
- Currency and billing — prices are rounded to the smallest unit a currency actually issues — the cent, for most — and the method used to round tax and interest calculations can shift totals by real, if usually tiny, amounts across millions of transactions.
- Scientific measurement — reporting more digits than an instrument can actually resolve implies a false precision; significant-figure rounding keeps a result honest about how precisely it was actually measured.
- Computing — computers store most decimal numbers as binary floating-point approximations, and rounding rules govern how those approximations get displayed and compared — part of why 0.1 + 0.2 famously does not print as exactly 0.3 in many programming languages.
A common mistake: rounding too early
Rounding intermediate results in a multi-step calculation, then feeding those rounded figures into the next step, compounds error in a way that rounding only the final answer does not. A tax calculation that rounds a subtotal, then rounds again after adding a fee, then rounds again after applying a discount, can land noticeably off from doing the full calculation first and rounding only once at the end. The safer habit is to keep full precision through every intermediate step and round only the number that gets displayed or reported.
What this assumes, and where it stops
Assumptions
- The input number is treated as exact — any imprecision in how it was measured or entered is not modelled.
Limitations
- Extremely large numbers of significant figures (beyond about 15) can run into floating-point precision limits inherent to how computers store decimal numbers.
Common questions
Why does 2.5 round to 2 with banker's rounding but 3 with standard rounding?
Standard "round half away from zero" always pushes an exact .5 up (2.5 → 3). Banker's rounding instead rounds to whichever neighbouring integer is even — 2.5 is equidistant from 2 and 3, and 2 is even, so it rounds to 2. The next case, 3.5, would round up to 4 (also even) rather than down.
What are significant figures?
The digits in a number that carry meaningful precision, starting from the first non-zero digit. 1,234 has 4 significant figures; 0.0012 has 2 (the leading zeros just place the decimal point). Rounding to significant figures preserves relative precision regardless of a number's magnitude, unlike rounding to a fixed number of decimal places.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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