Round any number — up, down, to nearest, banker's rounding, or to a specific multiple. Choose decimal precision from 0 to 10 places, or use significant figures. Free, step-by-step, no signup.
5 modes — Standard · Ceiling · Floor · Banker's · Nearest Multiple
What is Rounding? Rounding simplifies a number by reducing its precision. Choose from 5 methods: standard nearest, ceiling (always up), floor (always down), banker's rounding (half-to-even — used in finance and Python 3), or round to a specific multiple (5, 10, 25 etc.).
Quick Examples — click to load
Supports integers, decimals, negatives, and scientific values.
Free calculators for students — percentage, GPA, grade, fraction & more
Common scenarios where rounding is used — and which method to choose.
78.666...→78.7%Method: Round to Nearest, 1 decimal place
Grade reports and report cards display clean percentages. Common Core Grade 5 (5.NBT.A.4) standard.
$12.456→$12.45Method: Round Down (Floor), 2 decimal places
US retailers use floor rounding to display prices — the customer pays slightly less, improving perception.
$1 = €0.92341→€0.9234Method: Round to Nearest, 4 decimal places
Forex trading platforms and banks display exchange rates to 4 decimal places for accuracy.
15.7839 meters→15 metersMethod: Round Down (Floor), nearest integer
Construction uses floor rounding — always cut less material than needed, not more.
4.6667 average score→4.67Method: Round to Nearest, 2 decimal places
APA and research papers round means and standard deviations to 2 decimal places.
$18.333 tax amount→$18.34Method: Round Up (Ceiling), 2 decimal places
IRS rounding rules: amounts under 50 cents round down, 50 cents or more round up. Agencies use ceiling to avoid shortfall.
Avoid in financial billing — can cause systematic 0.5-cent discrepancies at scale.
Avoid for retail pricing — customers prefer the lower displayed price.
Avoid for quantities that must be sufficient — you may be short.
Avoid when users expect traditional .5-rounds-up behaviour without explanation.
Avoid when exact decimal precision matters more than alignment to a scale.
When the digit after the rounding position is exactly 5, banker's rounding (used in Python 3, IEEE 754, and financial systems) rounds to the nearest even number instead of always rounding up. Over thousands of calculations, this eliminates the systematic upward bias that standard rounding introduces.
Rounding .5 values to nearest integer — Standard vs Banker's
| Input | Standard Round | Banker's Round | Why |
|---|---|---|---|
| 0.5 | 1 | 0 | 0 is even ✓ |
| 1.5 | 2 | 2 | 2 is even ✓ |
| 2.5 | 3 | 2 | 2 is even ✓ |
| 3.5 | 4 | 4 | 4 is even ✓ |
| 4.5 | 5 | 4 | 4 is even ✓ |
| 5.5 | 6 | 6 | 6 is even ✓ |
Bias test: Standard rounding on these 6 values sums to 3+4+5+6+7+8 = 33. Banker's rounding sums to 2+4+4+6+6+8 = 30. The average of the inputs (0.5 to 5.5) is 3.0. Banker's average: 30÷6 = 3.0. Standard average: 33÷6 = 5.5. Banker's rounding correctly preserves the mean; standard rounding systematically biases upward.
Where Banker's Rounding is the Default
Formula: Math.round(number ÷ multiple) × multiple
83nearest 10 →80Grade rounding, time slots
147nearest 100 →100Budget estimates, population figures
13nearest 25 →25Pricing tiers, survey scales
17nearest 5 →15Scheduling intervals (15-min slots)
$4.97nearest 0.25 →$5.00Cash register rounding (quarters)
0.0073nearest 0.001 →0.007Scientific measurement rounding
These are different systems of precision. Decimal places count digits after the decimal point. Significant figures count all meaningful digits from the first non-zero digit — leading zeros never count, but trailing zeros after the decimal do.
| Number | 3 Decimal Places | 3 Sig Figs | Key Difference |
|---|---|---|---|
| 3.14159 | 3.142 (3 d.p.) | 3.14 (3 s.f.) | Same result here by coincidence |
| 0.00456 | 0.005 (3 d.p.) | 0.0046 (2 s.f.) | Leading zeros not counted in s.f. |
| 12345 | 12345 (0 d.p.) | 12300 (3 s.f.) | Trailing zeros added for sig figs |
| 0.1000 | 0.1 (4 d.p. → 0.1000) | 0.1000 (4 s.f.) | Trailing zeros after decimal count |
Use Decimal Places when:
Use Significant Figures when:
Each language and platform has different default rounding behaviour — and different gotchas that catch developers off-guard.
round(number, ndigits)Nearest
round(3.14159, 2) → 3.14Ceiling
import math; math.ceil(2.3) → 3Floor
math.floor(2.9) → 2⚠️ round(2.5) → 2 (banker's rounding, not 3). Use decimal.Decimal for financial work.
Math.round(n * 10^d) / 10^dNearest
Math.round(3.14159 * 100) / 100 → 3.14Ceiling
Math.ceil(2.3) → 3Floor
Math.floor(2.9) → 2⚠️ Math.round(2.45 * 10) / 10 → 2.4 (float precision). Use toFixed(n) for display only.
=ROUND(number, num_digits)Nearest
=ROUND(3.14159, 2) → 3.14Ceiling
=CEILING(2.3, 1) → 3Floor
=FLOOR(2.9, 1) → 2⚠️ CEILING and FLOOR take a significance argument, not decimal places. CEILING(2.3, 0.1) ≠ CEILING(2.3, 1).
ROUND(number, decimal_places)Nearest
ROUND(3.14159, 2) → 3.14Ceiling
CEILING(2.3) → 3Floor
FLOOR(2.9) → 2⚠️ Behaviour varies by database. PostgreSQL ROUND() on numeric vs. float types may differ. Always test edge cases.
These errors produce wrong results even when the formula looks correct.
Rounding 2.45 to 1 decimal place and getting 2.4 instead of 2.5
Floating-point precision issue. In binary, 2.45 is stored as 2.44999999... so Math.round() gives 2.4. This is not a bug — it is IEEE 754 floating-point arithmetic working as designed.
✓ Fix: Use Banker's Rounding for monetary values, or multiply by 10, round as integer, then divide back.
Using Round Down (Floor) for quantities that must be sufficient
If you need 14.2 meters of cable and floor to 14m, you will be 0.2m short. Floor always gives less than or equal to the true value.
✓ Fix: Use Round Up (Ceiling) whenever the rounded quantity must cover the full required amount.
Rounding intermediate results instead of the final answer
Each rounding step introduces error that compounds. E.g., 3.14 × 2.72 = 8.5408, but rounding first to 3.1 × 2.7 = 8.37 — an error of 0.17. In financial calculations across thousands of rows, this adds up significantly.
✓ Fix: Keep full precision throughout every calculation step. Round only the final output.
Assuming Python's round() works like standard rounding
Python 3's built-in round() uses Banker's Rounding (round half to even), not standard rounding. round(2.5) = 2, round(3.5) = 4. Developers moving from Python 2 or other languages are frequently caught by this.
✓ Fix: Use math.ceil(), math.floor(), or the Decimal module with ROUND_HALF_UP for traditional rounding behaviour in Python 3.
Rounding negative numbers — floor and ceiling behave oppositely
Floor of −2.3 is −3 (more negative), not −2. Ceiling of −2.7 is −2 (less negative), not −3. This surprises developers who assume floor = 'round down in magnitude.'
✓ Fix: Remember: floor always goes toward −∞, ceiling always goes toward +∞ — regardless of the sign of the number.
These documented real-world cases show how small rounding mistakes can compound into significant — sometimes catastrophic — failures. Each is a lesson in numerical precision.
What Happened
The US Patriot missile system tracked time using an integer counter measured in tenths of a second. This value was converted to a floating-point number, but the binary representation of 0.1 is non-terminating — causing a small rounding error of approximately 9.54 × 10⁻⁸ seconds per tick.
Consequence
After 100 hours of continuous operation, the accumulated error grew to 0.34 seconds. The system failed to track an incoming Iraqi Scud missile in Dhahran, Saudi Arabia. The missile struck a barracks, killing 28 US soldiers.
Lesson
Time systems must use exact integer arithmetic. Never accumulate floating-point representations of time-critical values.
What Happened
The Vancouver Stock Exchange (VSE) index was truncated (not rounded) to 3 decimal places after every transaction. The index started at 1,000 in January 1982.
Consequence
By November 1983, the index stood at 524.811 — seemingly a massive 47% loss. But when the 22 months of transactions were recalculated without truncation, the correct index was 1,098.892. The systematic truncation-vs-rounding error had quietly erased 574 points from the published index.
Lesson
Truncation is not the same as rounding. Financial systems must round, not truncate, and the rounding method should be explicitly defined in the system specification.
What Happened
The Ariane 5 rocket reused software from Ariane 4. A 64-bit floating-point value representing horizontal velocity was converted to a 16-bit signed integer. Ariane 5 flew a different trajectory and reached a velocity that was too large to fit in 16 bits.
Consequence
The conversion caused an operand overflow exception. The Inertial Reference System shut down. The rocket self-destructed 37 seconds after launch. The satellite payload and launcher cost approximately $500 million USD.
Lesson
Numeric conversions between types require explicit range checks. Software reuse across different physical environments requires full re-validation, including numerical edge cases.
Different industries have specific rounding conventions — often governed by regulations, professional standards, or safety requirements.
Example: 3.2 mg dose → 3.5 mg (next available tablet strength). Never give less than prescribed.
USP Chapter ⟨795⟩ pharmaceutical compounding guidelines
Example: $1,234,567.456 → $1,234,567.46 (round to nearest cent for all line items)
ASC 250 (GAAP) requires consistent rounding methodology disclosed in notes
Example: 14.3 kg/m² load → 14 kg/m² (conservative). 14.3 m of cable needed → 15 m ordered.
ASCE 7 and ACI 318 specify conservative (floor) rounding for structural loads
Example: When averaging millions of values, standard rounding biases the mean upward. Banker's rounding is symmetric.
IEEE 754 default rounding mode; used by numpy, pandas, R, and most statistical software
Example: $12.456 → $12.45 displayed to customer. Cost basis $8.333 → $8.34 for internal margin calc.
Common practice; varies by jurisdiction for consumer protection law compliance
How each rounding method is implemented and verified.
Common questions about rounding numbers — from basic concepts to professional and programming-specific scenarios.