Math · Estimation
Rounding
Calculator
Round any number to decimal places, significant figures, or nearest multiple. Supports 6 rounding modes with live results, number line visualization, and all-mode comparison.
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Result
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Rounding Error
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Mode
Round a Number
Round To
dp
Rounding Mode
Rounded Result
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Half-Up · 2 decimal places
Original
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Error
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Half-Up
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Ceiling
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Floor
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Truncate
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⚖️ All 6 Rounding Modes — Same Number
📏 Number Line Visualization
🔴 Floor
🟡 Original
🟢 Ceiling
🔵 Result (selected mode)
📐 Rounding Modes Reference
Half-Up (Standard)
≥0.5 → round up, <0.5 → round down
2.5→3, 2.4→2, −2.5→−2. Most common everyday rounding. Used in schools.
Half-Down
>0.5 → round up, ≤0.5 → round down
2.5→2, 2.6→3, −2.5→−3. Opposite of half-up for ties.
Half-Even (Banker's)
0.5 → round to nearest even
2.5→2, 3.5→4, 4.5→4. Minimizes statistical bias. Used in finance.
Ceiling (Always Up)
Always round toward +∞
2.1→3, −2.9→−2. Used in inventory (round up to ensure enough stock).
Floor (Always Down)
Always round toward −∞
2.9→2, −2.1→−3. Used in age calculation (floor of years lived).
Truncation (Toward Zero)
Drop digits, always toward 0
2.9→2, −2.9→−2. Used in integer division. Never increases magnitude.
Understanding Rounding
Rounding approximates a number to a simpler or shorter value while keeping it close to the original. It's used in everyday arithmetic, finance, science, and computing — any time exact precision is unnecessary or impractical.
Significant Figures vs Decimal Places
Decimal places: digits AFTER the decimal point
3.14159 to 2 dp = 3.14
0.00456 to 2 dp = 0.00 (not useful!)
Significant figures: meaningful non-zero digits
3.14159 to 3 sf = 3.14
0.00456 to 3 sf = 0.00456 (3 sig figs: 4, 5, 6)
12345 to 3 sf = 12300
Nearest multiple:
3.7 to nearest 5 = 5
137 to nearest 100 = 100 or 200 (→200, closer)
Why does 0.5 sometimes round down in programming?
Many programming languages use "banker's rounding" (half-even) by default — Python's built-in round(), IEEE 754 floating-point standard, and .NET all use this. So round(2.5) = 2 and round(3.5) = 4 (always toward even). This prevents statistical bias when rounding many numbers. If you need standard half-up rounding in Python, use the decimal module or math.floor(x + 0.5).
What is rounding error and how does it accumulate?
Rounding error is the difference between the original and rounded value. When you round many numbers and sum them, errors can accumulate. For example, rounding 100 values each with +0.5 error gives a total error of +50. Banker's rounding reduces this because half the 0.5 cases round up and half round down, canceling out. This is why financial calculations use banker's rounding.
When do you use significant figures instead of decimal places?
Use significant figures in science and engineering when the precision of a measurement matters regardless of scale. "3 significant figures" means 3 meaningful digits whether the number is 0.00456 or 456,000. Decimal places are better for fixed-unit quantities like currency ($2.50 = 2 decimal places always). Scientists always use sig figs; accountants always use decimal places.
How does ceiling differ from truncation for negative numbers?
For positive numbers, ceiling rounds up (2.3 → 3) and truncation rounds down (2.7 → 2). For negative numbers they differ: ceiling of −2.7 is −2 (toward +∞, less negative), while truncation of −2.7 is also −2 (toward zero). Floor of −2.3 is −3 (away from zero for negatives). The difference: ceiling always goes toward +infinity; truncation always goes toward zero.