Rounding
Calculator
Round any number to decimal places, significant figures, or the nearest ten, hundred, or thousand. Supports 6 rounding modes with live results, a number line, and an all-mode comparison.
3.14
RESULT
−0.00159
ROUNDING ERROR
Half-Up
MODE
Round a Number
Rounded Result
3.14
Half-Up · 2 decimal places
Rounding error: −0.00159
3.14159
Original
−0.00159
Error
3.14
Half-Up
3.15
Ceiling
3.14
Floor
3.14
Truncate
All 6 Rounding Modes — Same Number
Half-Up ✓
3.14
Round 0.5 and above up, below 0.5 down. Standard rounding — the everyday default taught in school.
Error: −0.00159
Half-Down
3.14
Round above 0.5 up, 0.5 exactly down. Opposite of half-up for ties.
Error: −0.00159
Banker's
3.14
Round 0.5 to the nearest even digit. Reduces statistical bias across repeated roundings.
Error: −0.00159
Ceiling
3.15
Always round toward +∞ (up for positive, "less negative" for negative).
Error: +0.00841
Floor
3.14
Always round toward −∞ (down for positive, "more negative" for negative).
Error: −0.00159
Truncate
3.14
Drop the extra digits, no rounding logic. Never increases the magnitude.
Error: −0.00159
Number Line Visualization
Target: 2 decimal places
Rounding Modes Reference
Half-Up (Standard)
≥0.5 → round up, <0.5 → round down
2.5→3, 2.4→2, −2.5→−3. 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→−2. Opposite of half-up for ties.
Half-Even (Banker's)
0.5 → round to nearest even digit
2.5→2, 3.5→4, 4.5→4. Minimizes statistical bias. Used in finance.
Always Up (Ceiling)
Always round toward +∞
2.1→3, −2.9→−2. Used in inventory (round up to ensure enough stock).
Always Down (Floor)
Always round toward −∞
2.9→2, −2.1→−3. Used in age calculation (floor of years lived).
Truncate (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 as close to the original as the target precision allows. It shows up constantly in everyday arithmetic, finance, science, and computing — anywhere exact precision is unnecessary, impractical, or simply more detail than the situation needs. The catch is that different rounding methods can produce different answers for the same number, and knowing which one applies (and why) matters more than most people realize. Standard half-up rounding is the everyday default most people learn in school, banker's rounding (half-to-even) is used where repeated rounding could otherwise introduce a systematic upward bias, and truncation shows up in some financial and programming contexts where any rounding at all is considered too generous.
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, whichever is closer)| Mode | Rule | Worked Example (round to whole number) |
|---|---|---|
| Half-Up (Standard) | Ties round away from zero | 2.5 → 3, −2.5 → −3 |
| Half-Down | Ties round toward zero | 2.5 → 2, −2.5 → −2 |
| Half-Even (Banker's) | Ties round to the nearest even digit | 2.5 → 2, 3.5 → 4 |
| Ceiling | Always toward +∞ | 2.1 → 3, −2.9 → −2 |
| Floor | Always toward −∞ | 2.9 → 2, −2.1 → −3 |
| Truncate | Drops digits, always toward zero | 2.9 → 2, −2.9 → −2 |
— FAQ