GST calculation: ₹89.255 with different rounding
Half-up: ₹89.26. Half-even: ₹89.26 (next digit is odd 5, rounds to even 6). Half-down: ₹89.25. Floor: ₹89.25. Ceiling: ₹89.26. Indian GST law usually requires half-up to nearest paise.
Rounding Calculator - Бесплатный онлайн-калькулятор
Round any number to a chosen number of decimal places using the rounding mode of your choice - half-up, half-down, half-even (banker's), ceiling, floor or truncate. Different modes give different results for tie cases (.5 boundary).
- Формула на странице
- Работает в браузере
- Ввод остаётся приватным
Negative = round to tens / hundreds
2.5 rounded to 0 decimal places (half-up)
3
All rounding modes
Half up (default)3
Half down2
Half even (banker's)2
Round up (ceil)3
Round down (floor)2
Truncate2
Часть содержимого пока показывается на английском.
Что такое Rounding Calculator
Rounding might sound trivial, but the rules subtly differ depending on context and can cause meaningful financial or computational discrepancies. School mathematics teaches the 'round half up' rule (2.5 becomes 3, 1.5 becomes 2). Banking and accounting use 'round half to even' (Banker's rounding) to avoid the systematic upward bias that hurts customers when applied repeatedly to interest, fees, and exchange rates. IEEE 754 floating-point (the standard for all computer arithmetic) uses round-half-even by default. JavaScript's Math.round() uses round-half-up. Excel uses round-half-up for the ROUND function but round-half-even internally. These differences cause confusion when results don't match across systems.
This calculator supports all six common rounding modes: half-up (school standard), half-down, half-even (banker's), ceiling (always toward +infinity), floor (always toward -infinity), and truncate (toward zero). For Indian taxation, banking, GST calculations, currency conversion, and salary computations, rounding rules are often explicitly specified in regulations - for example, GST law uses 'round to nearest paise', TDS rules round to nearest rupee, EMI rounds to nearest rupee. Knowing which mode to apply where prevents discrepancies.
Как пользоваться: Rounding Calculator, шагов: 4
Enter the number you want to round.
Pick the decimal places (negative values round to tens, hundreds, etc.).
Pick a rounding mode.
Read the rounded result.
Как работает Rounding Calculator
Most modes only differ when the value is exactly halfway between two roundings. Half-up always pushes 0.5 up. Half-even pushes to the nearest even digit (used in finance to avoid systematic upward bias). Ceiling and floor always go up or down regardless of value.
Formula
Half-up: round 0.5 up Half-even: round 0.5 to nearest even (banker's) Ceil/Floor/Trunc: ignore tie rule
- Half-upSchool standard, default in most software
- Half-evenIEEE 754 default, avoids upward bias
- TruncDrop the digits, no rounding
Как Rounding Calculator получает результат
Six standard rounding modes: (1) Half-up (school): 0.5 rounds to 1, 1.5 to 2, 2.5 to 3. Always pushes ties away from zero. (2) Half-even (banker's): 0.5 to 0, 1.5 to 2, 2.5 to 2, 3.5 to 4. Pushes ties to the nearest even - over many rounds, no systematic bias.
(3) Half-down: 0.5 rounds to 0, 1.5 to 1 - pushes ties toward zero. (4) Ceiling: always rounds toward positive infinity. ceil(2.3) = 3, ceil(-2.7) = -2. (5) Floor: always rounds toward negative infinity. floor(2.7) = 2, floor(-2.3) = -3. (6) Truncate: drop fractional part, toward zero. trunc(2.7) = 2, trunc(-2.7) = -2. Trunc and floor differ for negative numbers.
Decimal places parameter: 0 rounds to integer. Positive value rounds to that many decimal places (2 = round to paise, useful for GST and currency). Negative values round to powers of 10 (-1 = nearest 10, -2 = nearest 100, -3 = nearest 1000, -5 = nearest lakh). Useful for budgeting and rough estimates. The calculator handles all decimal place values gracefully including edge cases like rounding very small numbers and very large numbers.
Разобранные примеры
Banker's rounding for interest computation: ₹1245.555
Half-up: ₹1245.56. Half-even: ₹1245.56 (5 next; 5 is odd, so rounds to even 6). Used in financial systems to avoid bias when applied to billions of small calculations.
Rounding to nearest 1000 for budget: ₹47,389
Half-up with -3 decimal places: ₹47,000. Half-even: ₹47,000. Ceiling: ₹48,000. Floor: ₹47,000. Useful for high-level budget planning.
Когда использовать: Rounding Calculator
- GST calculations rounded to nearest paise.
- TDS and income tax computations rounded to nearest rupee.
- EMI calculations with currency rounding.
- Inventory and financial reporting precision.
- Scientific data reporting with significant figures.
- Statistical analysis - rounding probabilities for presentation.
- Budget planning - rounding to convenient round numbers.
- Banking interest computation - usually banker's rounding.
Типичные ошибки и подводные камни
- Using half-up everywhere when banker's rounding (half-even) is required by financial regulation.
- Confusing truncation with floor for negative numbers.
- Rounding intermediate values in long calculations. Round only at final display.
- Mixing rounding modes across systems (Excel vs JavaScript vs Python).
- Forgetting floating-point precision issues - 0.1+0.2 = 0.30000000000000004, round to fix display.
Как получить больше от инструмента
- Use banker's rounding (half-even) for any financial computation involving many small numbers.
- Use half-up for school math and everyday rounding.
- Round only at the final display step. Rounding intermediate values introduces compounding errors.
- For currency, round to 2 decimal places (paise). For budgets, round to thousands or lakhs.
- Pair with the percentage, scientific notation and statistics calculators on this site for related precision work.
Вопросы: Rounding Calculator
What is banker's rounding?
Half-even mode - when exactly at the halfway, round to the nearest even digit. So 2.5 rounds to 2; 3.5 rounds to 4. Used in finance and IEEE 754 to prevent the systematic bias of always rounding up.
Why does Excel sometimes round differently?
Excel's ROUND uses half-up. But the underlying IEEE 754 floating-point uses half-even, which can leak through in some operations. Use ROUNDUP or ROUND with explicit mode for predictable results.
Round to nearest 10, 100?
Use negative decimal places. -1 rounds to nearest 10, -2 to nearest 100, -3 to nearest 1000.
Trunc vs floor - same thing?
For positive numbers yes. For negatives they differ: floor(−1.5) = −2 (round toward −∞), trunc(−1.5) = −1 (toward zero).
Why doesn't 0.1 + 0.2 = 0.3?
Floating-point can't represent 0.1 exactly. The result is 0.30000000000000004. Round to a reasonable number of decimals to handle this.
Is rounding the same as truncation?
No. Truncation drops digits without considering the next digit's value. Rounding looks at the next digit to decide direction.
Math in your browser
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If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Rounding Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.