Rounding Calculator
Round numbers to specified decimal places. Shows rounded, floor, ceiling, and truncated values. See also Significant Figures Calculator and Decimal to Fraction.
How to Round Numbers
Rounding replaces a number with an approximate value that has fewer digits. Look at the digit immediately after your desired precision: if it is 5 or greater, round up; if it is less than 5, round down. Floor always rounds toward negative infinity, ceiling always rounds toward positive infinity, and truncation simply removes digits beyond the specified place.
Rounding Rules
Round half up (standard):
If digit ≥ 5 → round up
If digit < 5 → round down
Floor: always round toward −∞
Ceiling: always round toward +∞
Truncate: remove digits (round toward 0)
Example
Number: 3.14159
Round to 2 decimal places:
Rounded: 3.14 (digit after is 1, which is < 5)
Floor: 3.14
Ceiling: 3.15
Truncated: 3.14
Frequently Asked Questions
What is the difference between rounding and truncating?
Rounding considers the next digit to decide whether to go up or down. Truncating simply removes all digits beyond the specified place, always moving toward zero.
What happens when the digit is exactly 5?
Standard rounding (round half up) rounds 5 upward. Some systems use "round half to even" (banker's rounding) which rounds to the nearest even number to reduce bias.
How do floor and ceiling differ for negative numbers?
Floor rounds toward negative infinity (e.g., floor(−2.3) = −3), while ceiling rounds toward positive infinity (e.g., ceil(−2.3) = −2). Truncation rounds toward zero (e.g., trunc(−2.3) = −2).