Round any number to decimal places, significant figures, or the nearest 10/100/1000 — with five rounding modes including banker's rounding.
Results update live as you type.
3.14159 rounded to 2 d.p.
Original
3.14159
unchanged value
Lower bound
3.14
round-down option
Upper bound
3.15
round-up option
Abs. error
0.00159
|x − rounded|
| Mode | Behaviour at .5 | Example x = 2.5 |
|---|---|---|
| Half up (standard) | 0.5 rounds up | 3 |
| Half even (banker's) | 0.5 rounds to even | 2 |
| Half down | 0.5 rounds down | 2 |
| Ceiling | always up | 3 |
| Floor | always down | 2 |
| Truncate | toward zero | 2 |
The Method
Rounding to n decimal places is mathematically equivalent to round(x × 10n) ÷ 10n. The tie-break rule — half up, half even, etc. — decides what happens when the discarded digits are exactly 0.5. For significant figures, find the order of magnitude (k = ⌊log₁₀|x|⌋) and round to n − 1 − k decimal places. Rounding to the nearest 10 / 100 / 1000 / 0.05 uses the same trick with the appropriate multiplier.
Working for the current input
About This Tool
A rounding calculator takes any number and reduces its precision to a chosen target — a number of decimal places, a number of significant figures, or the nearest unit (10, 100, 1000, 0.5, 0.25, 0.05). It also lets you pick the tie-break rule: what to do when the discarded part is exactly 0.5.
Rounding shows up everywhere: cash payments round to the nearest 0.05 in many countries, scientific measurements are reported to the right number of significant figures, financial reports typically round to two decimal places, and statistics use rounding to keep numbers human-readable. Each of these contexts has a different convention — this calculator covers all of them.
The default mode is round half up, the rule almost everyone learns in school: 0.5 rounds up to 1, 1.5 to 2, 2.5 to 3. But there are real-world reasons to use other rules. Banker's rounding (round half to even) is the default in IEEE 754 floating-point arithmetic and in many statistical packages because it eliminates the small positive bias of always rounding 0.5 up. Ceiling, floor and truncate are used in inventory, capacity, and tax calculations where direction matters.
Use this free rounding calculator for finance, science, statistics, or programming — anywhere precision must be controlled. All calculation runs entirely in your browser.
Six Rounding Modes
Half up, half even (banker's), half down, ceiling, floor and truncate.
Many Targets
Decimal places, significant figures, nearest 10 / 100 / 1000 / 0.5 / 0.25 / 0.05.
Number-Line Visual
See exactly where your value sits between the two adjacent round numbers.
Error Display
Absolute error |x − rounded| shown alongside upper and lower bounds.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Step-by-Step Working
Each substitution and rounding decision shown — useful for homework.
Three inputs — value, target, mode — and you have a rounded answer with full working.
Enter any decimal value (positive or negative). The calculator handles tiny numbers, large numbers, and very precise inputs.
Choose decimal places, significant figures, or one of the nearest-unit presets (10, 100, 1000, 0.5, 0.25, 0.05).
If you picked d.p. or s.f., set n from 0 to 15. The places field disappears for nearest-unit targets.
Half up for everyday work, half even for statistics / IEEE 754, ceil / floor / trunc for capacity-style problems.
The big number is the rounded value. Stat tiles show the upper / lower bound and the absolute error.
The number-line view shows exactly where x sits between the two adjacent round numbers — and which one it rounds to.
Everything you need to know about rounding rules, significant figures, and edge cases.
The "round half up" rule is what most people learn in school: look at the first dropped digit — if it is 5 or more, round up; if 4 or less, round down. So 2.45 → 2.5 and 2.44 → 2.4. This is the default in this calculator and in most everyday contexts.
Banker's rounding rounds halves to the nearest even digit: 0.5 → 0, 1.5 → 2, 2.5 → 2, 3.5 → 4. This is the default in IEEE 754 floating-point arithmetic and in many statistical packages because, over many random values, it eliminates the small positive bias that "always round 0.5 up" introduces (the bias matters when summing or averaging large lists).
Find the first significant digit (the first non-zero digit reading left-to-right). Keep n digits starting from there and discard or round the rest. Example: 0.004321 to 2 s.f. is 0.0043; 5872 to 2 s.f. is 5900. Leading zeros never count as significant. The calculator does all this for you when you pick the "Significant figures" target.
Floor always rounds toward negative infinity (−1.5 → −2, 1.5 → 1). Ceiling always rounds toward positive infinity (−1.5 → −1, 1.5 → 2). Truncate always rounds toward zero (−1.5 → −1, 1.5 → 1). For positive numbers floor and truncate match; for negative numbers they differ.
Several countries (Australia, Canada, New Zealand, Switzerland) round cash totals to the nearest 0.05 at the till, because they no longer mint 1-cent coins. The same trick works for any "round to nearest fraction" — multiply by 1/step, round, then divide. The calculator's Nearest 0.05 preset does this in one step.
Because 0.1 and 0.2 cannot be represented exactly in binary floating-point — they become very long repeating fractions. The closest binary approximations add to 0.30000000000000004. This is a hardware-level issue (IEEE 754) and shows up in every programming language. Rounding the result back to a reasonable number of decimal places hides it for display.
Yes. The half-up / half-down modes preserve magnitude direction (so −2.5 rounds to −3 with half-up, −2 with half-down). Floor and ceiling behave according to their mathematical definitions — be careful with negatives, since floor(−1.5) = −2, not −1.
Excel and Google Sheets ROUND() uses round half away from zero (slightly different from half up — they match for positive numbers but differ for negatives). Both also offer ROUNDUP, ROUNDDOWN, MROUND (nearest multiple), and CEILING / FLOOR. This calculator's half up matches spreadsheet ROUND for positive values; pick ceiling or floor for the direction-specific variants.