Rounding Calculator – Every Rounding Rule in One Place
Rounding looks like the simplest operation in arithmetic until two people round the same number and get different answers. This rounding calculator takes any value and rounds it to a chosen number of decimal places, to the nearest whole number, or to the nearest arbitrary interval such as 0.25, 5 or 25. It then shows the result under all seven common rounding conventions at once, so you can see exactly where they agree and where they part company.
Three Rounding Targets
Decimal places is the everyday case: 3.14159 rounded to two decimals gives 3.14. Nearest integer drops the fractional part entirely, turning 47.386 into 47. Nearest multiple snaps a value onto a grid of your choosing — rounding 138 to the nearest 25 gives 150, because 138 is 13 away from 125 but only 12 away from 150. Multiple rounding is what you need for engineering tolerances, pricing tiers, time blocks and stock increments.
Why Rounding Modes Disagree
Every mode agrees on values that are clearly nearer one neighbour than the other. They only diverge on a tie — a value sitting exactly halfway, like 2.5. Round half up sends ties toward positive infinity, so 2.5 becomes 3 and -2.5 becomes -2. Round half away from zero, the version taught in most schools, pushes ties outward on both sides, giving 3 and -3. Round half down mirrors round half up toward negative infinity. This is why a spreadsheet, a database and a programming language can each report a different answer for the same input.
Banker's Rounding and Statistical Bias
Round half to even — usually called banker's rounding — resolves a tie by moving to whichever neighbour is even, so 2.5 becomes 2 while 3.5 becomes 4. Because ties then go up roughly half the time and down the other half, totals built from many rounded values do not creep upward the way they do under round half up. It is the default tie rule in the IEEE 754 floating-point standard and is widely used in accounting, tax reporting and statistical software for exactly that reason.
Ceiling, Floor and Truncate
The three directed modes ignore which neighbour is nearer. Ceiling always moves toward positive infinity, so 4.001 becomes 5. Floor always moves toward negative infinity, so 4.999 becomes 4. Truncate simply discards the remaining digits, which always moves toward zero. For positive numbers floor and truncate look identical, but negatives expose the difference: floor(-4.1) is -5 while truncate(-4.1) is -4.
1.00 when rounding 1.005 to two decimals, because binary floating point stores that value as a hair under 1.005. This tool converts the digits you type into exact integer arithmetic before deciding anything, so 1.005 correctly becomes 1.01 under round half up.Choosing the Right Mode
Use round half up or round half away from zero for grades, homework and everyday estimation. Use banker's rounding when many rounded numbers will be summed, such as invoice lines or survey statistics. Use ceiling when a shortfall is unacceptable — ordering materials, sizing containers, or counting how many buses a group needs. Use floor or truncate when you must never overstate a value, as with age in years, loyalty points earned or a quota that cannot be exceeded.
Batch Rounding and Sanity Checks
The batch field accepts a comma-, space- or newline-separated list and rounds every entry with the same settings, flagging individual values that cannot be parsed instead of rejecting the whole list. The reported difference between the original and rounded value is the rounding error you have introduced; adding those errors across a batch is the fastest way to see whether your chosen convention is quietly biasing a total in one direction.