Rounding Calculator

How to Use This Calculator

1. Enter the number to round and the decimal places to keep.
2. Select a rounding method — standard, ceiling, floor, truncate, or banker's.
3. Use the Standard Rounding tab to compare all four methods side-by-side.
4. Use Banker's Rounding tab to see exactly where standard and half-even differ.
5. Use Significant Figures tab to round to a given number of sig figs with scientific notation.
6. Professional tier: round to the nearest 5/10/25/0.25, and compare JavaScript vs Python behavior.

Formula

Example

Frequently Asked Questions

• What's the difference between rounding methods — nearest, up, down, and banker's? ▼
  Rounding half away from zero (standard) is what most people learn in school: 2.5 rounds to 3, -2.5 rounds to -3. Round up (ceiling) always moves toward positive infinity regardless of the fractional part — Math.ceil(2.1) = 3, Math.ceil(-2.9) = -2. Round down (floor) always moves toward negative infinity — Math.floor(2.9) = 2, Math.floor(-2.1) = -3. Truncation cuts the decimal without regard for size — Math.trunc(2.9) = 2, Math.trunc(-2.9) = -2. Banker's rounding (half-even) rounds 0.5 cases to the nearest even integer: 2.5 → 2, 3.5 → 4, 4.5 → 4, 5.5 → 6. The purpose of banker's rounding is to eliminate systematic bias. Standard rounding always rounds 0.5 up, so in a large dataset half-values always bias the sum upward. Banker's rounds half-values up half the time and down half the time (to even), so the cumulative bias averages to zero. This is why it is used in financial systems, IEEE 754 floating-point arithmetic, and Python's built-in round() function.
• Why does Python round 2.5 to 2 instead of 3? ▼
  Python's round() function implements banker's rounding (half-even), not the standard half-away-from-zero. This is an intentional design decision: round(2.5) = 2 (rounds to even), round(3.5) = 4 (rounds to even), round(4.5) = 4 (rounds to even). This surprises most beginners who expect 2.5 to round to 3. The reason Python chose this approach is statistical correctness — when rounding large datasets of values with 0.5 fractional parts, always rounding up introduces a systematic positive bias. By alternating between rounding up (odd to even) and rounding down (even stays even), banker's rounding produces zero net bias over many operations. A secondary issue is floating-point representation: 2.5 is exactly representable in binary (1/2 is a power of 2), so Python really does see 2.5. But values like 0.1 are not exactly representable in binary floating-point, so round(0.15, 1) may not behave as expected due to representation error — 0.15 is actually stored as slightly less than 0.15, causing it to round to 0.1 rather than 0.2 in some implementations.
• When should I use banker's rounding vs standard rounding? ▼
  Use banker's rounding (half-even) when you are accumulating many rounded values and care about avoiding systematic bias — financial calculations, statistical sampling, scientific measurements, and any large-scale numeric computation. The IEEE 754 floating-point standard mandates half-even as the default rounding mode for this reason. Banking and accounting systems use it to ensure that rounding errors do not systematically favor one party. Use standard rounding (half away from zero) when you need to match conventional expectations — educational contexts, everyday calculations, displaying single values to users, and any situation where the half-case is rare. Standard rounding is simpler to explain and implement mentally. Use ceiling (always up) when you need conservative overestimates — calculating room for safety margins, determining how many containers you need (you cannot use 2.3 boxes, so round up to 3). Use floor (always down) when truncating to whole units — reporting completed hours worked, age in years. Use truncation (toward zero) in integer division contexts and when you want to simply discard the fractional part.
• How do I round to the nearest 5 or 10? ▼
  To round to the nearest N, divide by N, apply standard rounding, then multiply by N. For the nearest 10: round(137 / 10) x 10 = round(13.7) x 10 = 14 x 10 = 140. For the nearest 5: round(137 / 5) x 5 = round(27.4) x 5 = 27 x 5 = 135. This works for any N, including decimals: to round 1.876 to the nearest 0.25, compute round(1.876 / 0.25) x 0.25 = round(7.504) x 0.25 = 8 x 0.25 = 2.00. Common applications: rounding prices to the nearest 0.05 or 0.25 cent in cash transactions, rounding measurements to the nearest 1/8 inch in construction, rounding timestamps to the nearest 15 minutes in scheduling, rounding survey scores to the nearest 0.5 for cleaner reporting. In spreadsheets, Excel's MROUND(value, multiple) does this directly — MROUND(137, 5) = 135. In Python: round(value / n) x n, or use the decimal module for precision control.
• Why does floating-point rounding sometimes give unexpected results? ▼
  Floating-point numbers in computers use binary (base-2) representation, which cannot exactly represent many decimal fractions. The same way 1/3 = 0.333... never terminates in base-10, values like 0.1, 0.2, and 0.3 never terminate in base-2. The value 0.1 is stored as approximately 0.1000000000000000055511151231257827. This means operations that seem exact produce tiny errors: 0.1 + 0.2 = 0.30000000000000004 in most languages. When rounding is applied, these tiny representation errors can push a value just above or below a 0.5 boundary, producing unexpected results. For example, round(0.15, 1) may give 0.1 instead of 0.2 because 0.15 is stored as slightly less than 0.15. Solutions: use the decimal module in Python (arbitrary-precision decimal arithmetic), use BigDecimal in Java, format the result to a fixed number of decimal places and parse back, or work in integer cents rather than decimal dollars for monetary calculations. The key insight is that floating-point rounding errors are not bugs in the rounding function — they reflect the fundamental imprecision of binary floating-point representation.

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