Rounding Calculator
Round any number using 8 different rounding methods, or round to the nearest fraction like 1/8.
Round to a fraction
Round a decimal to the nearest 1/n — e.g. the nearest 1/8 for shop measurements.
What is rounding?
Rounding replaces a number with a shorter approximation at a chosen level of precision — nearest whole number, nearest tenth, nearest thousand. What makes rounding interesting is the tie-break: what should happen with an exact half like 2.5, or a negative half like −5.5? Different rules give different answers, and picking the right one matters in accounting, science and engineering. This calculator supports eight tie-break methods plus a separate rounding-to-fractions tool.
Rounding calculator, piece by piece
Each card explains one of the tie-break families the calculator offers, plus the fraction tool below the main rounder. Try the same input with different methods to see where they agree and where they diverge.
Half-up / half-down — nearest with a tie rule
Most everyday rounding: pick the nearer integer for non-ties, and for an exact half use the tie rule. Half up sends the tie toward +∞ (so 2.5 → 3 and −2.5 → −2). Half down is the mirror. Half-away-from-zero and half-toward-zero are two more tie rules the calculator offers.
Ceiling and floor — one-way rounding
Ceiling always moves toward +∞ and floor always toward −∞, regardless of how close the input is to the next integer. Use them when you need a guaranteed upper bound (ceiling) or lower bound (floor) — for example, how many buses fit a group or how many whole tiles cover a floor.
Half to even — banker's rounding
Ties round to the nearest even integer, so 2.5 → 2 and 3.5 → 4. Because half the ties go up and half go down, sums and averages accumulate less bias than always-up rounding. It's the IEEE 754 floating-point default and the standard in accounting.
Round to a fraction
The second tool rounds a decimal to the nearest 1/n — 1/8, 1/16, 1/32 — the way engineering, shop and imperial measurements quantise sizes. Internally it scales by n, rounds to the nearest whole number, then divides back.
Features of this calculator
- Eight rounding methods, each with correct handling of negative numbers
- Choose precision from thousands down to millionths, or any custom decimal place
- A separate rounding-to-fractions tool for engineering and shop measurements
- Full explanation of the method applied to your number
Frequently asked questions
+What is banker's rounding and why is it used?
Banker's rounding (round half to even) breaks ties by rounding to the nearest even integer. Because half the ties round up and half round down, sums and averages accumulate less bias than always-up rounding. It is the IEEE 754 floating-point default and standard in accounting.
+How does rounding work with negative numbers?
It depends on the method. Ceiling always moves toward +∞ so −5.01 → −5. Floor always moves toward −∞ so −5.01 → −6. 'Half up' means toward +∞ for ties (−5.5 → −5) while 'half away from zero' means −5.5 → −6.
+What is the difference between half up and half away from zero?
For positive numbers they give the same answer. For negatives they diverge: half up rounds −2.5 to −2, half away from zero rounds −2.5 to −3.
+How do I round to the nearest 1/8?
Multiply by 8, round to the nearest integer, then divide by 8. Use the fraction tool above to do this automatically.
+Which method should I pick?
Everyday: half up or half away from zero. Repeated financial or scientific rounding: half to even. Guaranteed upper/lower bound: ceiling or floor.