Floor Function Calculator

The floor function maps a real number to the greatest integer that is less than or equal to it. It is commonly written with floor brackets, but this calculator displays the notation as floor(x) for clarity in plain text. For a positive decimal such as 3.14, the greatest integer no larger than the input is 3. For an exact integer such as 5, the floor remains 5 because the input already satisfies the definition. Negative values reveal why the floor function is more precise than simply saying round down. The floor of -2.7 is -3, not -2. On a number line, -3 is the greatest integer that is still less than or equal to -2.7. Truncating the decimal digits would instead produce -2, which is greater than the original value and therefore cannot be its floor. Thinking in terms of movement toward negative infinity avoids this common mistake. Floor values are useful whenever a calculation must count only complete units. If 17 items are packed into groups of 5, only 3 complete groups can be made. If 185 seconds are converted into complete minutes, flooring 185 divided by 60 gives 3. Programmers use the same principle for pagination, array indexing, grid coordinates, time conversion, bucketing continuous measurements, and extracting integer parts under a clearly defined negative-number rule. The floor function differs from the ceiling function and ordinary rounding. Ceiling returns the smallest integer greater than or equal to the input, so ceiling of 3.14 is 4 and ceiling of -2.7 is -2. Ordinary nearest-integer rounding chooses whichever integer is closest and needs a tie-breaking convention for half values. Floor always follows one unambiguous direction regardless of distance. This calculator accepts positive numbers, negative numbers, decimals, and integers. It uses the browser's standard finite-number representation, so extremely long decimal inputs may be rounded internally before the floor is evaluated. For normal mathematical, educational, engineering, and programming values, the result directly follows the formal definition. You can verify an answer by checking that the result is an integer no greater than the input and that adding one to it would make it greater than the input.